Edge Coloring Research Articles

A Comparative Study of Fuzzy Domination and Fuzzy Coloring in an Optimal Approach

An optimal network refers to a computer or communication network designed, configured, and managed to maximize efficiency, performance, and effectiveness while minimizing cost and resource utilization. In a network design and management context, optimal typically implies achieving the best possible outcomes between various factors. This research investigated the use of fuzzy graph edge coloring for various fuzzy graph operations, and it focused on the efficacy and efficiency of the fuzzy network product using the minimal spanning tree and the chromatic index of the fuzzy network product. As a network made of nodes and vertices, measurement with vertices is a parameter for domination, and edge measurement is a parameter for edge coloring, so we used these two parameters in the algorithm. This paper aims to identify an optimal network that can be established using product outcomes. This study shows a way to find an optimal fuzzy network based on comparative optimal parameter domination and edge coloring, which can be elaborated with applications. An algorithm was generated using an optimal approach, which was subsequently implemented in the form of applications.

More on online weighted edge coloring

We revisit online weighted edge coloring. In this problem, weighted edges of a graph are presented one by one, to be colored with positive integers. It is required that for every vertex, all its edges of every common color will have a total weight not exceeding 1. We provide an improved upper bound on the performance of a greedy algorithm First Fit for the case of arbitrary weights, and for the case of weights not exceeding 12. Here, the meaning of First Fit is that every edge is colored with a color of the smallest index that will keep the coloring valid. This improves the state-of-the-art with respect to online algorithms for this variant of edge coloring. We also show new lower bounds on the performance of any online algorithm with weights in (0,1t], for any integer t≥2.

A Tool to Assist in the Analysis of Gaze Patterns in Upper Limb Prosthetic Use

Gaze-tracking, where the point of regard of a subject is mapped onto the image of the scene the subject sees, can be employed to study the visual attention of the users of prosthetic hands. It can show whether the user pays greater attention to the actions of their prosthetic hand as they use it to perform manipulation tasks, compared with the general population. Conventional analysis of the video data requires a human operator to identify the key areas of interest in every frame of the video data. Computer vision techniques can assist with this process, but fully automatic systems require large training sets. Prosthetic investigations tend to be limited in numbers. However, if the assessment task is well-controlled, it is possible to make a much simpler system that uses the initial input from an operator to identify the areas of interest and then the computer tracks the objects throughout the task. The tool described here employs colour separation and edge detection on images of the visual field to identify the objects to be tracked. To simplify the computer’s task further, this test uses the Southampton Hand Assessment Procedure (SHAP) to define the activity spatially and temporarily, reducing the search space for the computer. The work reported here concerns the development of a software tool capable of identifying and tracking the points of regard and areas of interest throughout an activity with minimum human operator input. Gaze was successfully tracked for fourteen unimpaired subjects and was compared with the gaze of four users of myoelectric hands. The SHAP cutting task is described and the differences in attention observed with a greater number of shorter fixations by the prosthesis users compared to unimpaired subjects. There was less looking ahead to the next phase of the task by the prosthesis users.

Rainbow Connection Number of Double Quadrilateral Snake Graph

Let graph G = be a non trivial connected graph. A graph G with edge coloring is called a rainbow connection, if for every pair of vertices on a path has a different color. The rainbow connection number denoted by is the minimum color needed to make graph G rainbow connection. In this study, we will determine the rainbow connection number of double quadrilateral snake graph and alternate double quadrilateral snake graph. The research results show that while if and if

First Report of Bipolaris zeae Causing Leaf Spot on Setaria viridis in China.

Green bristlegrass (Setaria viridis) is an annual dominant herb in arid sandy grasslands with strong drought resistance to water stress (Valença et al. 2020). In August 2021, brown or dark tan spots on the leaves of S. viridis were observed on natural grassland in Qingyang city, Gansu Province, China (36.55°N, 107.32°E). Leaf disease incidence was around 13%, and the infected area of each leaf was about 20%. For isolation, 30 tissue pieces (5×5 mm) from 10 symptomatic leaf samples were surface-sterilized with 70% ethanol for 30 seconds and rinsed three times with steriled distilled water. Then these tissues were placed on the potato dextrose agar (PDA) at 25 °C, and incubated in dark from 2 to 5 days. Sixteen single-spored cultures with consistent colony characteristics were obtained by single spore isolation as described in Manamgoda et al. (2012). Colonies on PDA were irregular shapes with black color and white edge; conidia were dark brown with septate, cylindrical, straight or flexuous geniculate at the upper end, 22.7 to 69.38×9.2 to 17.6 µm (n = 50; average size 40.8×13.2 µm) under microscope (40X). The internal transcribed spacer (ITS) and glyceraldehyde-3-phosphate dehydrogenase (GPD) regions of the representative isolate 83HXGWC, 84HXGWC and 85HXGWC were amplified using the primers of ITS1/ITS4 and GPD1/GPD2 (Manamgoda et al. 2012). All the amplified gene sequences were deposited into GenBank with accession numbers ITS (OP703331, OQ978850, and OQ978851) and GPD (OQ559683, OQ992505, and OQ992506). BLAST analysis of both the two segments showed 100% identity with those reported sequences of ex-type isolate BRIP 11512 (KJ415538 and KJ415408) of B. zeae Sivan (Tan et al. 2014; Bhunjun et al. 2020), respectively. In the maximum-likelihood phylogenetic tree, 83-HXGWC, 84HXGWC and 85HXGWC strains were grouped with the reference sequences of B. zeae with a high bootstrap supporting values of 100%. Five healthy green bristlegrass (6 weeks) plants in pots were sprayed with conidial suspensions (1×106 conidia ml-1). Another five pots were sprayed with sterilized distilled water (controls). Then all pots were individually covered with transparent polyethylene bags for 5 days to maintain high relative humidity and placed in a greenhouse maintained at 18 to 25 °C. After incubation for 14 days, the typical symptoms of leaf spots developed from brown to dark brown on the plants inoculated with conidial suspension, whereas no symptoms were observed on the control plants. The measurement of pathogenicity was carried out three times. The same pathogens were consistently reisolated from inoculated leaves, and was confirmed as B. zeae based on morphological and molecular analyses, fulfilling Koch's postulates. This study provides a new record of B. zeae on green bristlegrass on natural grassland in China, which can potentially impose disease challenges to other crops. Since, B. oryzae has been known to cause disease in cereal crops (Manamgoda et al. 2014), this can be a potential alternate source of survival of this pathogen.

A structural approach to the graceful coloring of a subclass of trees

Let M={1,2,..m} and G be a simple graph. A graceful m-coloring of G is a proper vertex coloring of G using the colors in M which leads to a proper edge coloring using M∖{m} colors such that the associated color of each edge is the absolute difference between their end vertices. The graceful chromatic number χg(G)= min {m:G admits a gracefulm− coloring }. We prove that 5≤χg(T)≤7, where T is a tree with Δ=4. Furthermore, we categorize the trees into three types along with its characterization and the related coloring algorithm are presented in this study.

A color edge extraction method on color image

A color edge extraction method on color image

Proper Edge Colorings of Cartesian Products with Rainbow C_4-s

Related to the famous (7,4)-problem, in an earlier paper we introduced B-colorings. We call a proper edge coloring of a graph G a B-coloring if every 4-cycle of G is colored with four different colors. Let q_B(G) denote the smallest number of colors needed for a B-coloring of G. Here we look at q_B(G) for Cartesian products of paths and cycles. Our main result is that q_B(G) is equal to the chromatic index of G for grids, i.e. for Cartesian products of paths (apart from a few exceptions). This extends an earlier result for the case when G is the d-dimensional cube. Our main tool is a lemma which gives q_B(Gsquare H)le q_B(G)+q_B(H) if chi (G)le q_B(H), chi (H)le q_B(G), where chi (G) is the chromatic number of G.

Investigate the Impact of the Current Watercolour Painting Market Situation on the Development of the Watercolour Painting Market in China. Market Environment as a Mediator

Purpose: The purpose of this study is to investigate the impact of the current watercolour painting market situation in China on the development of the watercolour painting market in China. In addition, this study investigates the role of the watercolour painting market environment in China as a moderating variable in the relationship between the current state of the watercolour painting market in China and its future development. Theoretical framework: Contemporary Chinese art and culture exist in a society that is open and pluralistic. Through the efforts of several generations, they have created not only a magnitude but also a vast market. In a technologically based society, technologically based painting is on the verge of extinction. The construction of cultural artistic conception and character is a novel topic in the art education and instruction of contemporary Chinese watercolour painting. Design/Methodology/Approach: A total of 495 respondents participated in the survey comprised of 110 watercolour artist collectors, 220 watercolour paintings and 165 lectors and business intermediaries 165. This study was a cross-sectional study where the data collection period is from August to October 2021. A survey with a closed-ended and self-administered format was conducted in order to collect data. The questionnaire is divided into two sections, Smart PLS was used to analyse the data and identify any significant relationships between the variables. There was a correlation between being a colour artist and collecting watercolour paintings. Findings: This study focuses on watercolour painters, watercolour collectors, and commercial intermediaries., according to the findings. This suggests that artists are more likely than non-artists to collect watercolour paintings. In addition, the study revealed that business intermediaries play a crucial role in facilitating the sale of these paintings. The study revealed that watercolour painting is a popular art form among both artists and collectors. Watercolour paintings have been a popular art form for centuries, and this study confirms that their popularity remains strong among both artists and collectors. The delicate beauty of watercolours, with their translucent washes of colour and soft edges, is particularly appealing to those who appreciate the subtleties of art. Research, practical & social implications: This study found that watercolour paintings are highly valued by business intermediaries, who recognize their potential as investments. In fact, many galleries and auction houses specialize in selling watercolours, and the market for these works continues to grow. Originality/Value: it is important to note that not all watercolour paintings are created equal - some are more highly prized than others based on factors such as the artist's reputation, the quality of the materials used, and the subject matter depicted. Overall, this study underscores the enduring appeal of watercolour paintings and their continued relevance in today's art world. This research provides valuable insights into the relationship between colour artists, collections of watercolour paintings, and art industry intermediaries.

Historical Factors Influencing Water Colour Painting Market Environment and Development in China Market Supervisor as a Moderator

Purpose: China has a long history of art, including watercolour painting, which has garnered international acclaim. China can gain recognition for its artistic accomplishments and contribute to the global art community by preserving and promoting the practise of watercolour painting both domestically and internationally. Theoretical framework: The tale of the development of Chinese watercolour painting is intricate and multidimensional, reflecting the impact of several historical events (Li, 2023; Yin,2022). These elements have all contributed to the creation of this stunning and lasting art form, from the rich philosophical and cultural traditions of China to the impact of aesthetic trends and technical advancements. Design/Methodology/Approach: A total of 495 respondents participated in the survey comprised of 110 watercolour artist collectors, 220 watercolour paintings and 165lectors and business intermediaries 165. This study was a cross-sectional study where the data collection period is from August to October 2021. Using Smart PLS, the collected data is analysed. Findings: The study revealed that watercolour painting is a popular art form among both artists and collectors. Watercolour paintings have been a popular art form for centuries, and this study confirms that their popularity remains strong among both artists and collectors. The delicate beauty of watercolours, with their translucent washes of colour and soft edges, is particularly appealing to those who appreciate the subtleties of art. Research, practical & social implications: This study found that watercolour paintings are highly valued by business intermediaries, who recognize their potential as investments. In fact, many galleries and auction houses specialize in selling watercolours, and the market for these works continues to grow. Originality/Value: It is important to note that not all watercolour paintings are created equal - some are more highly prized than others based on factors such as the artist's reputation, the quality of the materials used, and the subject matter depicted. Overall, this study underscores the enduring appeal of watercolour paintings and their continued relevance in today's art world.

The distinguishing index of graphs with infinite minimum degree

AbstractThe distinguishing index of a graph is the least number of colors necessary to obtain an edge coloring of that is preserved only by the trivial automorphism. We show that if is a connected ‐regular graph for some infinite cardinal then , proving a conjecture of Lehner, Pilśniak, and Stawiski. We also show that if is a graph with infinite minimum degree and at most vertices of degree for every infinite cardinal , then . In particular, if has infinite minimum degree and order at most .

Decomposing graphs into interval colorable subgraphs and no-wait multi-stage schedules

A graph G is called interval colorable if it has a proper edge coloring with colors 1 , 2 , 3 , … such that the colors of the edges incident to every vertex of G form an interval of integers. Not all graphs are interval colorable; in fact, quite few families have been proved to admit interval colorings. In this paper we introduce and investigate a new notion, the interval coloring thickness of a graph G , denoted θ int ( G ) , which is the minimum number of interval colorable edge-disjoint subgraphs of G whose union is G . Our investigation is motivated by scheduling problems with compactness requirements, in particular, problems whose solution may consist of several schedules, but where each schedule must not contain any waiting periods or idle times for all involved parties. We first prove that every connected properly 3-edge colorable graph with maximum degree 3 is interval colorable, and using this result, we deduce an upper bound on θ int ( G ) for general graphs G . We demonstrate that this upper bound can be improved in the case when G is bipartite, planar or complete multipartite and consider some applications in timetabling.

Royal Colorings of Graphs

For a graph \(G\) and a positive integer \(k\), a royal \(k\)-edge coloring of \(G\) is an assignment of nonempty subsets of the set \(\{1, 2, \ldots, k\}\) to the edges of \(G\) that gives rise to a proper vertex coloring in which the color assigned to each vertex \(v\) is the union of the sets of colors of the edges incident with \(v\). If the resulting vertex coloring is vertex-distinguishing, then the edge coloring is a strong royal \(k\)-coloring. The minimum positive integer \(k\) for which a graph has a strong royal \(k\)-coloring is the strong royal index of the graph. The primary emphasis here is on strong royal colorings of trees.

Equitable Edge Coloring of Splitting Graph of Some Classes of Wheel Graphs

The coloring of all the edges of a graph G with the minimum number of colors, such that the adjacent edges are allotted a different color is known as the proper edge coloring. It is said to be equitable, if the number of edges in any two color classes differ by atmost one. In this paper, we obtain the equitable edge coloring of splitting graph of W n , D W n and G n by determining its edge chromatic number.

Royal Colorings of Graphs

For a graph G and a positive integer k , a royal k -edge coloring of G is an assignment of nonempty subsets of the set { 1 , 2 , … , k } to the edges of G that gives rise to a proper vertex coloring in which the color assigned to each vertex v is the union of the sets of colors of the edges incident with v . If the resulting vertex coloring is vertex-distinguishing, then the edge coloring is a strong royal k coloring. The minimum positive integer k for which a graph has a strong royal k -coloring is the strong royal index of the graph. The primary emphasis here is on strong royal colorings of trees.

Ramsey Numbers of Large Even Cycles and Fans

For graphs $F$ and $H$, the Ramsey number $R(F, H)$ is the smallest positive integer $N$ such that any red/blue edge coloring of $K_N$ contains either a red $F$ or a blue $H$. Let $C_n$ be a cycle of length $n$ and $F_n$ be a fan consisting of $n$ triangles all sharing a common vertex.In this paper, we prove that for all sufficiently large $n$,\[R(C_{2\lfloor an\rfloor}, F_n)= \left\{ \begin{array}{ll}(2+2a+o(1))n & \textrm{if $1/2\leq a< 1$,}\\(4a+o(1))n & \textrm{if $ a\geq 1$.}\end{array} \right.\]

Equitable Edge Coloring of Splitting Graph of Some Classes of Wheel Graphs

The coloring of all the edges of a graph \(G\) with the minimum number of colors, such that the adjacent edges are allotted a different color is known as the proper edge coloring. It is said to be equitable, if the number of edges in any two color classes differ by atmost one. In this paper, we obtain the equitable edge coloring of splitting graph of \(W_n\), \(DW_n\) and \(G_n\) by determining its edge chromatic number.

Straight-line drawings of 1-planar graphs

A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. However, there are 1-planar graphs that do not admit a straight-line 1-planar drawing. We show that every 1-planar graph has a straight-line drawing with a two-coloring of the edges such that edges of the same color do not cross. Thus 1-planar graphs have geometric thickness two. In addition, the drawing is nearly 1-planar, that is, it is 1-planar if all fan-crossed edges are removed. An edge is fan-crossed if it is crossed by edges with a common vertex if it is crossed more than twice. The drawing algorithm uses high precision arithmetic with numbers with O(nlog⁡n) digits and computes the straight-line drawing from a 1-planar drawing in linear time on a real RAM.

Injective edge coloring of graphs with maximum degree 5

Injective edge coloring of graphs with maximum degree 5

An Experimental Study on Translucent Concrete

Abstract: This experimental study of translucent concrete which has the property of transmitting light from concrete by using optical fibers. Since years concrete has a low impression because of its dirty greyish colour , opaqueness and sharp edge but this concept has been changed after the development of light emitting concrete, which gives the increased strength, better looks and light transmitting features. Plastic optical fibers are used because of its total internal reflection as its working principle as it gives maximum efficiency in transmitting light. This report deals about the introduction of translucent concrete, materials used for making translucent concrete such as fine concrete, cement, optical fiber and procedure of making is also discuss for translucent concrete. After the study of different research paper results respected to 5%, 10% and 15% replacement of aggregate with optical fiber is discuss in this study.