Spider Graph Research Articles

Polygon-circle and word-representable graphs

We describe work on the relationship between the independently-studied polygon-circle graphs and word-representable graphs.A graph G = (V, E) is word-representable if there exists a word w over the alpha-bet V such that letters x and y form a subword of the form xyxy ⋯ or yxyx ⋯ iff xy is an edge in E. Word-representable graphs generalise several well-known and well-studied classes of graphs [S. Kitaev, A Comprehensive Introduction to the Theory of Word-Representable Graphs, Lecture Notes in Computer Science 10396 (2017) 36–67; S. Kitaev, V. Lozin, “Words and Graphs”, Springer, 2015]. It is known that any word-representable graph is k-word-representable, that is, can be represented by a word having exactly k copies of each letter for some k dependent on the graph. Recognising whether a graph is word-representable is NP-complete ([S. Kitaev, V. Lozin, “Words and Graphs”, Springer, 2015, Theorem 4.2.15]). A polygon-circle graph (also known as a spider graph) is the intersection graph of a set of polygons inscribed in a circle [M. Koebe, On a new class of intersection graphs, Ann. Discrete Math. (1992) 141–143]. That is, two vertices of a graph are adjacent if their respective polygons have a non-empty intersection, and the set of polygons that correspond to vertices in this way are said to represent the graph. Recognising whether an input graph is a polygon-circle graph is NP-complete [M. Pergel, Recognition of polygon-circle graphs and graphs of interval filaments is NP-complete, Graph-Theoretic Concepts in Computer Science: 33rd Int. Workshop, Lecture Notes in Computer Science, 4769 (2007) 238–247]. We show that neither of these two classes is included in the other one by showing that the word-representable Petersen graph and crown graphs are not polygon-circle, while the non-word-representable wheel graph W5 is polygon-circle. We also provide a more refined result showing that for any k ≥ 3, there are k-word-representable graphs which are neither (k −1)-word-representable nor polygon-circle.

Construction project productivity assesment model and its implementation in Indonesia construction industry

The increase of global competition in the world of construction forced construction companies to increase their productivity. One of the most important parts of the construction project is productivity. It is absolutely necessary to have a thorough research on the construction project productivity (CPP), so that contractors know the productivity level of their projects. This assessment has an effect on increasing the productivity of a construction project until it achieves the highest level of the construction project productivity. The purpose of this study is to propose a construction project productivity assesment model. In this study, project productivity variables are obtained by conducting in-depth literature review and structured interview with construction experts. Pairwise comparison is used to determine the factor weight. The final assessment is represented in the form of a web spider graph. To validate the model, several building projects in Indonesia are used as a case study. The weight for the CPP assessment at the internal level was 73.8% at an external rate of 26.2%. At the internal level, there are 2 categories namely: management category for 39.38% and human category for 34.42%. CPP results in Indonesia are the highest in the category of human variable worker turnover and availability while the lowest is in the category of management inspection delays.

Which cospectral graphs have same degree sequences

Two graphs are said to be L-cospectral (respectively, Q-cospectral) if they have the same (respectively, signless) Laplacian spectra, and a graph G is said to be L−DS (respectively, Q−DS) if there does not exist other non-isomorphic graph H such that H and G are L-cospectral (respectively, Q-cospectral). Let d1(G)≥d2(G)≥⋯≥dn(G) be the degree sequence of a graph G with n vertices. In this paper, we prove that except for two exceptions (respectively, the graphs with d1(G)∈{4,5}), if H is L-cospectral (respectively, Q-cospectral) with a connected graph G and d2(G)=2, then H has the same degree sequence as G. A spider graph is a unicyclic graph obtained by attaching some paths to a common vertex of the cycle. As an application of our result, we show that every spider graph and its complement graph are both L−DS, which extends the corresponding results of Haemers et al. (2008), Liu et al. (2011), Zhang et al. (2009) and Yu et al. (2014).

Maximizing general first Zagreb and sum-connectivity indices for unicyclic graphs with given independence number

In this paper it is shown that in the class of unicyclic graphs of order n and independence number s, the spider graph SΔ(n, s) is the unique graph maximizing general first Zagreb index 0Rα(G) for α > 1 and general sum-connectivity index χα(G) for α ≥ 1.

Abelian spiders and real cyclotomic integers

If Γ \Gamma is a finite graph, then the largest eigenvalue λ \lambda of the adjacency matrix of Γ \Gamma is a totally real algebraic integer ( λ \lambda is the Perron-Frobenius eigenvalue of Γ \Gamma ). We say that Γ \Gamma is abelian if the field generated by λ 2 \lambda ^2 is abelian. Given a fixed graph Γ \Gamma and a fixed set of vertices of Γ \Gamma , we define a spider graph to be a graph obtained by attaching to each of the chosen vertices of Γ \Gamma some 2 2 -valent trees of finite length. The main result is that only finitely many of the corresponding spider graphs are both abelian and not Dynkin diagrams, and that all such spiders can be effectively enumerated; this generalizes a previous result of Calegari, Morrison, and Snyder. The main theorem has applications to the classification of finite index subfactors. We also prove that the set of Salem numbers of “abelian type” is discrete.

Path multicoloring in spider graphs with even color multiplicity

We give an exact polynomial-time algorithm for the problem of coloring a collection of paths defined on a spider graph using a minimum number of colors (Min-PMC), while respecting a given even maximum admissible color multiplicity on each edge. This complements a previous result on the complexity of Min-PMC in spider graphs, where it was shown that, for every odd k, the problem is NP-hard in spiders with admissible color multiplicity k on each edge. We also obtain an exact polynomial-time algorithm for maximizing the number of colored paths with a given number of colors (Max-PMC) in spider graphs with even admissible color multiplicity on each edge.

Functional Food Formulation by the Addition of Whole Grain Flour and Linseed

Recommendations for consuming industrialized whole grain foods have been encouraged. The present study produced new functional foods and sought to identify the sensory profile of the foods processed. Four types of dried spaghetti were manufactured with different formulas, regarding their whole grain flour and linseed content (10 and 20%). For evaluation of the products obtained, the following methods were employed: sensory analysis of acceptance using a 9-point hedonic scale, applied to 50 trained judges, and Quantitative Descriptive Analysis (QDA) using a 9-cm unstructured line scale. Results were analyzed by ANOVA and Tukey’s test at 5% significance, and the sensory profile was expressed in the form of a spider graph. Acceptance test revealed no difference between the pasta containing 10% and 20% of whole grain and 10% of linseed. Results indicate acceptance of the 20% whole grain product regarding its raw texture and consistency when cooked, in addition to the possibility for the manufacture and acceptance of 10% linseed spaghetti.

A framework of fuzzy integrated MADM and GMA for maintenance strategy selection based on agile enabler attributes

BackgroundMaintenance cost of machinery, equipment and tooling are main contributor to total cost of production in processing industry. The aim of study is to explore selection of optimum maintenance strategy for steam generating unit (SGU) in a coal fired thermal power plant using various MADM and graphical approach. The novelty of research work is selection of strategy based on agile enabler attributes and use of graphical approaches for decision making. This selection procedure allows for speedy conflux of large number of attributes, which gives the decision maker an effective tool select optimum strategy.Case descriptionThe practicality of the framework has been justified through implementation in thermal power plant, situated in northern part of India. The plant has total installed capacity of 2400 MW. It has eight units. The present study is done in unit number 8.Discussion and evaluationThis selection is based on agile enabler attributes. Triangular fuzzy number (TFN) is used to take care of imprecise and vague judgements. For ranking of maintenance strategies MADM approaches of fuzzy AHP (FAHP), fuzzy TOPSIS (FTOPSIS); and Graphical approaches of Line graph and spider graph are used, respectively.ConclusionPDM has been ranked first by all evaluating approaches. There is also synergy in results. The proposed work not only provides the best alternative but also alternative ranking. The results will be shared with management for implementation so as to increase system availability and reduce operation cost.

The impact of home care nurses’ numeracy and graph literacy on comprehension of visual display information: implications for dashboard design

To explore home care nurses' numeracy and graph literacy and their relationship to comprehension of visualized data. A multifactorial experimental design using online survey software. Nurses were recruited from 2 Medicare-certified home health agencies. Numeracy and graph literacy were measured using validated scales. Nurses were randomized to 1 of 4 experimental conditions. Each condition displayed data for 1 of 4 quality indicators, in 1 of 4 different visualized formats (bar graph, line graph, spider graph, table). A mixed linear model measured the impact of numeracy, graph literacy, and display format on data understanding. In all, 195 nurses took part in the study. They were slightly more numerate and graph literate than the general population. Overall, nurses understood information presented in bar graphs most easily (88% correct), followed by tables (81% correct), line graphs (77% correct), and spider graphs (41% correct). Individuals with low numeracy and low graph literacy had poorer comprehension of information displayed across all formats. High graph literacy appeared to enhance comprehension of data regardless of numeracy capabilities. Clinical dashboards are increasingly used to provide information to clinicians in visualized format, under the assumption that visual display reduces cognitive workload. Results of this study suggest that nurses' comprehension of visualized information is influenced by their numeracy, graph literacy, and the display format of the data. Individual differences in numeracy and graph literacy skills need to be taken into account when designing dashboard technology.

Screening and preventing risks of frailty in community-dwelling senior citizens: a global personalised approach to promote healthy ageing

Concept and theory: multi-domains prevention at early stageFrailty is defined today within two main paradigms.The traditional approach considers frailty as an exclusively physical condition. This frailty syndrome represents declines in physiologic reserves and functions as well as resistance to stressors, leading to increased vulnerability and adverse health events. A person is said frail if three or more of the following criteria are present: unintentional weight loss, self-reported exhaustion, weakness (grip strength), slow walking speed, and low physical activity (Fried LP, 2001).The second paradigm includes the psychological and social domains of frailty, shifting from a vision of frailty as a phenotype to frailty as an accumulation of deficits in various domains: cognition, mood, motivation, motor skills, balance, capacity to carry out day-to-day activities, nutrition, social status and comorbidities (Rockwood K, 2005). A more recent model defines frailty as “a dynamic state affecting individuals with losses through one or more functional domains (physical, psychological and social), increasing overall the risk of adverse outcomes"(Gobbens RJ, 2010).Inspired by this multidimensional paradigm, the CARSAT concentrates its efforts on the risks of frailty, far preceding the state of acknowledged frailty (Noguès M, 2015). Through a global approach, we aim to improve frailty prevention by targeting individuals who, although still in good health, might be at risk of frailty. This implies transforming the traditional vision of primary, secondary and tertiary prevention (often leading to segmentation) into a more evolving and comprehensive process, based on the consideration of health from three dimensions: physiological, social and environmental. From this integration of social and health approaches at an early stage, individually-tailored responses are possible.Integrated care in practise: the concerted window serviceThe Regional Institute of Ageing (IRV) was founded by the CARSAT. This community, gathering regional experts and institutional stakeholders of the field, implemented in 2014 an experimental territorial project to offer global support to insured retirees or pre-retirees at risk of frailty.Individuals at risk of frailty are identified through the IRV's Frailty Observatory (geographic information system) or through other various social security organisations, and are then invited to present themselves. The aim is to provide advice and facilitate the access to rights and to social or health services, in partnership with the care sector. This concept is the concerted window service. The innovation is the possibility of crossing data from the health and the social sectors, enabled by a national decree of April 2015. Seniors who are part of this follow-up are given a personalised and regular monitoring every six months.As the number of individuals followed keeps growing, we aim to transfer this competency to regional stakeholders (institutions, foundations, health and wellbeing associations) by enabling them to act as concerted window services. The CARSAT will continue to ensure the coordination, the training of professionals, the research and the evaluation.CARSAT LR has adopted this concept as a pilot project and will thus be requested to ensure its diffusion at a national level as from the beginning of 2016. The principle has already been validated by the national authorities. The dissemination of this concerted window approach to all French regions is expected to be carried out shortly.Our tool: the active and healthy ageing spiderIn order to identify the real needs of the person entering the concerted window service and guide them to the appropriate services, the prevention case manager conducts a 45 min interview with the help of a multidimensional assessment tool (42-questions grid) built upon the EIP-AHA questionnaire (Bousquet, 2015).Individuals who are part of this follow-up will benefit from a dynamic evaluation of their individual risks of frailty, according to a 4-items assessment tool named the «frailty risks star» (5 questions per item). This grid may be utilised by a caregiver, case manager or even the senior himself. The results are transcribed every six months and the simple observation of the spider graph can establish links between the 4 items identified. The current observations made on 500 cases highlight the relevance of the instrument: it is user friendly and constitutes a valuable tool for professionals.It is designed to become an ICT tool (both the initial grid and the dynamic star), to be used by the regional stakeholders accompanying seniors, including in remote areas.

On Graceful Spider Graphs with at Most Four Legs of Lengths Greater than One

A graceful labeling of a tree T with n edges is a bijection f:V(T)→{0,1,2,…,n} such that {|f(u)-f(v)|:uv∈E(T)} equal to {1,2,…,n}. A spider graph is a tree with at most one vertex of degree greater than 2. We show that all spider graphs with at most four legs of lengths greater than one admit graceful labeling.

Success Factors of Online Learning Videos

Videos have emerged as a dominant medium for educational purposes in many Massive Open Online Course (MOOC) platforms. Online learning videos are visual components of the online learning platforms. They are particularly interesting for students who are visual learners and who learn best by watching the short format engaging videos rather than by just reading or listening to course materials. The paper focuses on the categorization of factors that are responsible for the success/popularity of online learning videos. The research is based on the literature review and video observations of the MOOC platforms, in particular of the Khan Academy and Coursera. In this paper, we propose a tabular and a spider graph as a condensed overview of categories that should commonly be utilized by the online learning video production to make them successful.

Channel Assignment Algorithms for Graphs in the Plane with Graceful Constraints

ABSTRACT An assignment of integer numbers to the vertices of a given graph under certain conditions is referred to as a graph labeling. The assignment of labels from the set {0,1,2,...,2 1} q to the vertices of G (with ( ) nVG vertices and ( ) q E G edges) such that, labelingwhen each edge has assigned a label defined by the absolute difference of its end-points, the resulting edge labels are 1,3 ,2 1 q is referred to as an odd graceful labeling of the graph. In 2000, Kathiresan [13] used the notation Pnm ; to denote the graph (spider graph) obtained by identifying the end points of m paths each one has length n , we use the notation C n ; m to denote the graph (closed spider) obtained by identifying the other end points of the graph . In this article, we present three algorithms to show how to odd gracefully label the vertices and the edges of the following graphs; P r m 2 1; rm , 1 5, 2 , the closed spider , and the graphs obtained by joining one or two paths

Rational method for 3D manufacturing tolerancing synthesis based on the TTRS approach “R3DMTSyn”

During the production of new part in an industrial environment, it results in a high percentage of scrap if manufacturing planning is not carried out properly. One of the major factors responsible for this phenomenon is tolerance synthesis. In this paper, we deal with tolerance synthesis, and especially tolerance type identified after transfer. An algorithmic Rational method for 3D Manufacturing Tolerancing Synthesis (R3DMTSyn), which is based on the use of the Technologically and Topologically Related Surface (TTRS) rules, is developed. The TTRS concept helps to generate only the necessary manufacturing specification needed to guarantee the respect of the functional specification studied. The manufacturing project is modeled by a graphical representation called the SPIDER GRAPH. With the SPIDER GRAPH, all active surfaces can be detected (machined and positioning surfaces), so it is possible to identify the location of the functional surfaces used in each functional specification. The construction or the determination of the tolerancing torsor, belonging to each active surface, contributes to the selection of the adequate case of associations. A semantic study is already done to identify all possible combinations or associations needed to locate surfaces during each phases. Finally, referring to the developed TTRS_Cars_Process and in every phase, one or more manufacturing specifications are generated until finishing the treatment of all surfaces (surface belonging to the functional condition, or intermediate surfaces).

Profiling the Leadership of Project Managers

Leadership is a concept rooted in human relationships, personal experience, and introspection. Teaching leadership, therefore, is best done by placing students in simulated situations where each individual can recognize within a short time the systemic consequences of personal behaviors and actions affecting others. A 52-action-card game was developed for this purpose. The game reveals a “player's” current management or leadership preferences and also elicits questioning and team discussion of the consequences of alternative actions. The cards provide a choice of actions that are plausible in responding to a deeply troubled construction project. Unbeknown to the players, each suite of action cards represents a different style. The game consists of selecting and recording 10 action cards, which, first in the opinion of the individual and then by consensus after vigorous team discussion and negotiation, will improve the troubled construction project. The individually selected cards are plotted on a four quadrant spider graph, profiling the students' leadership and management preferences, both at the beginning and at the end of the course or seminar. By selecting again 10 preferred action cards at the conclusion of a session, any shift in preferences can be assessed.

Bottom Up: A Modular View of Immunology

In this issue of Immunity, Chaussabel et al. (2008) apply an inductive approach to pathway discovery identifying modular units that govern human immune biology.

Community participation in primary health care projects of the Muldersdrift Health and Development Programme

After numerous teething problems (1974-1994), the Department of Nursing Education of WITS University took responsibility for the Muldersdrift Health and Development Programme (MHDP). The nursing science students explored and implemented an empowerment approach to community participation. The students worked with MHDP health workers to improve health through community participation, in combination with primary health care (PHC) activities and the involvement of a variety of community groups. As the PHC projects evolved over time, the need arose to evaluate the level of community participation and how much community ownership was present over decision-making and resources. This led to the question "What was the level of community participation in PHC projects of the MHDP?" Based on the question the following objectives were set, i.e. (i) to evaluate the community participation in PHC initiatives; (ii) to provide the project partners with motivational affirmation on the level of community participation criteria thus far achieved; (iii) to indicate to participants the mechanisms that should still be implemented if they wanted to advance to higher levels of community participation; (iv) to evaluate the MHDP's implementation of a people-centred approach to community participation in PHC; and (v) the evaluation of the level of community participation in PHC projects in the MHDP. An evaluative, descriptive, contextual and quantitative research design was used. Ethical standards were adhered to throughout the study. The MHDP had a study population of twenty-three (N=23) PHC projects. A purposive sample of seven PHC initiatives was chosen according to specific selection criteria and evaluated according to the "Criteria to evaluate community participation in PHC projects" instrument (a quantitative tool). Structured group interviews were done with PHC projects' executive committee members. The Joint Management Committee's data was collected through mailed self-administered questionnaires. Validity and reliability were ensured according to strict criteria. Thereafter results were analysed and plotted on a radiating arm continuum. The following factors had component scores: organization, leadership, resources, management; needs and skills. A spider graph was produced after each factor's continuum was connected in a spoke figuration that brought them together at the base where participation was at its most narrow. The results are presented and a graph and discussion is provided on each of the PHC projects. The research results indicated that although community participation was broadened, there was minimal success in forcing a shift in power over decision-making and resources. This demonstrated that power over planning and resources should remain in the hands of the partners if community participation was to remain progressive and sustained. Results furthermore indicated that the people-centred approach to With regard to the Joint Management Committee's evaluation of community participation, it was concluded that power over decision-making and resources remained with health professionals rather than with the community, and that a people-centred approach had not been adopted.

Spidergraph

Spidergraph

Tough spiders

AbstractSpider graphs are the intersection graphs of subtrees of subdivisions of stars. Thus, spider graphs are chordal graphs that form a common superclass of interval and split graphs. Motivated by previous results on the existence of Hamilton cycles in interval, split and chordal graphs, we show that every 3/2‐tough spider graph is hamiltonian. The obtained bound is best possible since there are (3/2 – ε)‐tough spider graphs that do not contain a Hamilton cycle. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 23–40, 2007

A Mixed-Integer Programming Approach to Air Cargo Fleet Planning

This paper deals with the mathematical programming aspects of a long range planning study done for the Flying Tiger Line, an all-cargo airline. The study addressed two strategic problems: the design of the service network and the selection and deployment of the aircraft fleet. We show how the concept of a spider graph provides a natural building block for network design and present a mixed-integer programming model that enables the planner to evaluate any network constructed from spider graphs by determining the most profitable selection of aircraft and routing of cargo.