Tree Graph Research Articles

Construction Of an Ideal Topological Space From Undirected Graphs

Graph theory, which is used effectively in many field from science to liberal arts, has very important place in our lives. As a result of this , the ideal topological structure of the graphs is studied by many researchers. In this paper ,investigate the topological spaces generated by cycle graph. The ideal topological space is obtained by deleting one of the edges of the cycle graph, then we take the largest tree graph through its vertices , we get the ideal topological space.

Impact assessment of unsustainable airport development in the Himalayas using remote sensing: A case study of Pakyong Airport, Sikkim, India

Ground deformation is a widespread phenomenon that accelerates due to anthropogenic land development. Thus reclaimed/created land is more vulnerable to deformation and subsidence, especially in mountain areas. Advanced Differential Synthetic Aperture Radar Interferometry (A-DInSAR) can be used to monitor such projects. The Pakyong Airport is an engineering feat, constructed by cutting a mountain and converting it into a tabletop in a landslide-prone zone and seismically active region of the Sikkim Himalayas. The cutting of hill slopes for airport construction and other anthropogenic activities has increased slope instability in the region. This paper studies the slow-moving landslides in the airport neighbourhood using A-DInSAR on Sentinel-1 time series data consisting of 64 images of ascending track and 82 images of the descending track. The time period of monitoring was from October 2014 to April 2018 (43 months). The images have been connected using the Minimum Spanning Tree graph for interferogram generation for estimating deformation. The atmospheric noise was removed, and the results enabled the identification of deformation (in line-of-sight) on the airstrip as well as in the neighbouring area, both the upslope and downslope of the airport. The deformation rates estimated were up to ±90 mm/year in Pakyong from both tracks. We could successfully capture such land movement associated with the Pakyong Airport construction and help assess the impacts of infrastructure construction on the slope stability of the area. The controlling factors such as precipitation, seismicity, geology and others were analysed with respect to the deformation obtained. This study helps in assessing the land deformation after construction (cutting and filling of the slope) in the area. The deformation detected in this study needs to be addressed for the safety of the residents as well as for the infrastructure present in the area.

Local multiset dimension of corona product on tree graphs

One of the topics of distance in graphs is resolving set problem. This topic has many applications in science and technology namely navigation robots, chemistry structure, and computer sciences. Suppose the set [Formula: see text], the vertex representations of [Formula: see text] is [Formula: see text], where [Formula: see text] is the length of the shortest path of the vertex [Formula: see text] and the vertex in [Formula: see text] together with their multiplicity. The set W is called a local [Formula: see text]-resolving set of graphs G if [Formula: see text] for [Formula: see text]. The local [Formula: see text]-resolving set having minimum cardinality is called the local multiset basis and its cardinality is called the local multiset dimension of [Formula: see text], denoted by [Formula: see text]. In our paper, we determine the establish bounds of local multiset dimension of graph resulting corona product of tree graphs.

On the study of rainbow antimagic connection number of comb product of tree and complete bipartite graph

Rainbow antimagic coloring is the combination of antimagic labeling and rainbow coloring. The smallest number of colors induced from all edge weights of antimagic labeling is the rainbow antimagic connection number of [Formula: see text], denoted by [Formula: see text]. Given a graph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text], the function [Formula: see text] from [Formula: see text] to [Formula: see text] is a bijective function. The associated weight of an edge [Formula: see text] under [Formula: see text] is [Formula: see text]. A path [Formula: see text] in the vertex-labeled graph [Formula: see text] is said to be a rainbow [Formula: see text] path if for any two edges [Formula: see text] it satisfies [Formula: see text]. The function [Formula: see text] is called a rainbow antimagic labeling of [Formula: see text] if there exists a rainbow [Formula: see text] path for every two vertices [Formula: see text]. When we assign each edge [Formula: see text] with the color of the edge weight [Formula: see text], we say the graph [Formula: see text] admits a rainbow antimagic coloring. In this paper, we show the new lower bound and exact value of the rainbow antimagic connection number of comb product of any tree and complete bipartite graph.

Bogoliubov-de Gennes equation on graphs: A model for tree-branched Majorana wire network

We consider Bogoliubov-de Gennes equation on a metric tree graph. Formulation of the problem for arbitrary graph topology is provided. Self-adjoint vertex boundary conditions are derived. Exact solutions of the problem is obtained for quantum tree graph. A quantum graph based model for tree-branched Majorana wire network is proposed.

코로나19(COVID-19)를 전후로 한 코스닥(KOSDAQ) 종목들의 수익률 상관관계 변동에 대한 구조적 분석

In this study, the Minimum spanning tree (MST) method was applied to daily price data of KOSDAQ stocks to conduct a structural analysis of changes in each graph and degree based on before and after COVID-19 occurred and at the start of each pandemic. As a result, it was confirmed that the minimum height tree graph and order change were the greatest before and after the outbreak of COVID-19 and at the beginning of the first and second pandemic, and stock market stabilized as of the start of the third pandemic as COVID-19 entered a prolonged period. These results confirmed that the change in the correlation between stocks increased at a time when social turmoil was the biggest, and that the stock market gradually stabilized at some point when the situation caused by social confusion entered a prolonged period.

The number of spanning trees in a k5 chain graph

Spanning trees (ST) have numerous applications in various fields, including computer science, graph theory, network design, and optimization. ST uses in designing efficient network topologies. In computer networks, a ST ensures that all nodes are connected while avoiding loops and redundant connections. This helps in minimizing network congestion and ensuring reliable communication. In routing protocols the ST’s play a crucial role such as the Spanning Tree Protocol (STP) and Rapid Spanning Tree Protocol (RSTP). These protocols are used to prevent network loops and establish a loop-free topology for efficient packet forwarding. In image processing the ST’s have applications in algorithms such as image segmentation and region merging. By constructing a minimum spanning tree based on pixel intensities or other image features, regions or objects can be efficiently grouped together. In wireless sensor networks, ST’s are employed to organize the network structure, reduce energy consumption, and enable efficient data collection. By constructing a spanning tree, sensor nodes can communicate with a central node or sink node while minimizing energy consumption and prolonging network lifetime. Motivated by the above applications and by the normalized Laplacian (NL) matrix, we obtained the spectrums of the n copies of K 5 chain graph, and is denoted by . By utilizing these spectrums, we have successfully calculated the number of spanning trees for .

An Efficient Dynamic Programming Algorithm for Finding Group Steiner Trees in Temporal Graphs

The computation of a group Steiner tree (GST) in various types of graph networks, such as social network and transportation network, is a fundamental graph problem in graphs, with important applications. In these graphs, time is a common and necessary dimension, for example, time information in social network can be the time when a user sends a message to another user. Graphs with time information can be called temporal graphs. However, few studies have been conducted on GST in terms of temporal graphs. This study analyzes the computation of GST for temporal graphs, i.e., the computation of temporal GST (TGST), which is shown to be an NP-hard problem. We propose an efficient solution based on a dynamic programming algorithm for our problem. This study adopts new optimization techniques, including graph simplification, state pruning, and A ∗ search, are adopted to dramatically reduce the algorithm search space. Moreover, we consider three extensions for our problem, namely the TGST with unspecified tree root, the progressive search of TGST, and the top-N search of TGST. Results of the experimental study performed on real temporal networks verify the efficiency and effectiveness of our algorithms.

Generalized cut trees for edge-connectivity

We present three cut trees of graphs, each of them giving insights into the edge-connectivity structure. All three cut trees have in common that they are defined with respect to a given binary symmetric relation R on the vertex set of the graph, which generalizes Gomory-Hu trees. Applying these cut trees, we prove the following:•A pair of vertices {v,w} of a graph G is pendant if λ(v,w)=min⁡{d(v),d(w)}. Mader showed in 1974 that every simple graph with minimum degree δ contains at least δ(δ+1)/2 pendant pairs. We improve this lower bound to δn/24 for every simple graph G on n vertices with δ≥5 or λ≥4 or vertex connectivity κ≥3, and show that this is optimal up to a constant factor with regard to every parameter.•Every simple graph G satisfying δ>0 has O(n/δ)δ-edge-connected components. Moreover, every simple graph G that satisfies 0<λ<δ has O((n/δ)2) cuts of size less than min⁡{32λ,δ}, and O((n/δ)⌊2α⌋) cuts of size at most min⁡{α⋅λ,δ−1} for any given real number α≥1.•A cut is trivial if it or its complement in V(G) is a singleton. We provide an alternative proof of the following recent result of Lo et al.: Given a simple graph G on n vertices that satisfies δ>0, we can compute vertex subsets of G in near-linear time such that contracting these vertex subsets separately preserves all non-trivial min-cuts of G and leaves a graph having O(n/δ) vertices and O(n) edges.

Shock induced variable density flows in the vacuum microchannel: I. medium laser fluence

Laser-matter interactions with metal target cause plasma explosion and shock accelerated variable density flow instabilities in the Semiconfined Configuration (SCC). Their study gives deeper insight into the flow instabilities present in all microchannel devices. Blast wave motion along the SCC microchanel causes the Kelvin–Helmholtz (KH) instability and formation of vortex filaments for the critical Reynolds number. Appearing in all shear layers—it affects the fluid transport efficiency. Shear layer acceleration causes a Raleigh-Taylor instability (RTI). Oriented bubble growth by discrete merging indicates anisotropic RTI mixing. Similar RTI flame instability appears in the conversion of chemical energy into electricity affecting microcombustion efficiency. Another case of anisotropic RTI is the flow boiling for cooling of chips and microelectronic devices. The RTI boiling which appears for the critical heat flux is based on rising surface vapor columns (oriented bubble growth) with liquid counterflow (spike prominences) for the critical wavelength at density interface. The RT bubble merging graph trees determine turbulent mixing which affects the heat transfer rates. Bottom-wall turbulent flow in the SCC microchannel causes streaks of the low momentum fluid and formation of hairpin vortex packets with lattice organization. This makes possible to quantify parameters responsible for the evolution of hairpin vortex packets in the microchannel devices. Appearing from the low to the high Reynolds numbers they affect the transport properties, control of the fluid motion, enhancement of mixing, or the separation of fluids. Fluid particle ejecta—thin supersonic jets - evolve into long needle-like jets which start spiraling, helical pairing and swirling in the field of thermal gradients. Such instabilities appear in the microcombustion flame instability and in the space micropropulsion systems. Oscillating and spiral flames appear in the presence of thermal gradient in the microchannel, due to the combined effects of thermal gradient fields and the mixture flow rates.

Spanning trees in graphs without large bipartite holes

AbstractWe show that for any $\varepsilon \gt 0$ and $\Delta \in \mathbb{N}$ , there exists $\alpha \gt 0$ such that for sufficiently large $n$ , every $n$ -vertex graph $G$ satisfying that $\delta (G)\geq \varepsilon n$ and $e(X, Y)\gt 0$ for every pair of disjoint vertex sets $X, Y\subseteq V(G)$ of size $\alpha n$ contains all spanning trees with maximum degree at most $\Delta$ . This strengthens a result of Böttcher, Han, Kohayakawa, Montgomery, Parczyk, and Person.

Topological structure of functions with isolated critical points on a 3-manifold

To each isolated critical point of a smooth function on a 3-manifold we put in correspondence a tree (graph without cycles). We will prove that functions are topologically equivalent in the neighbourhoods of critical points if and only if the corresponding trees are isomorphic. A complete topological invariant of functions with fore critical points, on a closed 3-manifold, was constructed. A criterion for the topological equivalence of functions with a finite number of critical points on 3-manifolds is given.

The evolution of cooperation in the unidirectional division of labour on a tree network.

Division of labour on complex networks is rarely investigated using evolutionary game theory. We investigate a division of labour where divided roles are assigned to groups on the nodes of a general unidirectional finite tree graph network. From the network's original node, a task flows and is divided along the branches. A player is randomly selected in each group of cooperators and defectors, who receives a benefit from a cooperator in the upstream group and a part of the task. A cooperator completes their part by paying a cost and then passing it downstream until the entire task is completed. Defectors do not do anything and the division of labour stops, causing all groups to suffer losses due to the incomplete task. We develop a novel method to analyse the local stability in this general tree. We discover that not the benefits but the costs of the cooperation influence the evolution of cooperation, and defections in groups that are directly related to that group's task cause damage to players in that group. We introduce two sanction systems, one of which induces the evolution of cooperation more than the system without sanctions, and promote the coexistence of cooperator and defector groups.

The Number of Spanning Trees of General Fan Graphs

As we all know, the number of spanning trees can be calculated by virtue of the famous Kirchhoff’s matrix-tree theorem. However, it doesn’t work when coming across complex graphs with thousands of edges and vertices or more. Hence, how to obtain accurate solutions of the number of spanning trees of general fan graphs becomes a subject to several studies of many places like computer science, physics and mathematics. In this paper, we focus on calculating different types of graphs generated by adding vertices and edges to the fan graph. Particularly, we define a new graph called "C-graph", which brings a unique angle of view for us to recognize the construction of original graphs. Moreover, we introduce a new iterative relation about the general fan graph, simplifying the calculation. Therefore, we can obtain functions of the number of spanning trees obtained from given fan graphs, which are also suitable for larger and more complex conditions. Finally, we discuss the effect of vertices and edges on the number of spanning trees, finding out that edges have greater impact. Additionally, by using Kirchhoff’s matrix-tree theorem, we verified the rationality of our results.

Potential outcome and decision theoretic foundations for statistical causality

Abstract In a recent work published in this journal, Philip Dawid has described a graphical causal model based on decision diagrams. This article describes how single-world intervention graphs (SWIGs) relate to these diagrams. In this way, a correspondence is established between Dawid's approach and those based on potential outcomes such as Robins’ finest fully randomized causally interpreted structured tree graphs. In more detail, a reformulation of Dawid s theory is given that is essentially equivalent to his proposal and isomorphic to SWIGs.

Graceful labeling construction for some special tree graph using adjacency matrix

Graceful labeling construction for some special tree graph using adjacency matrix

A New Tree Graph Method for Synthesizing Planetary Gear Trains of Vehicle Powertrains

The function of vehicle powertrains is to transmit power from the power source (engine or electric machine) to the output shaft. Different torques and speeds of the output shaft are achieved through the structure of planetary gear train (PGT). The performance of a powertrain depends on the choice of topological structure of the PGT to a large extent. The topological synthesis of PGTs is of great significance to the design of new powertrains. A tree graph method for the topological synthesis of PGTs is proposed in this paper. Firstly, the rules for generating (N + 1)-link tree graphs from N-link tree graphs are proposed. Then, the method for adding geared edges into the tree graph is presented, and topological graphs of 1-DOF PGTs are directly synthesized from their tree graphs. A unified algorithm applicable for both open-loop and closed-loop graphs is proposed to eliminate isomorphic tree graphs and topological graphs of PGTs. The complete atlases of tree graphs and topological graphs of 1-DOF PGTs with three to ten links are obtained for the first time.

Особливості розрахунку очікуваної вартості дослідно-конструкторських робіт зі створення космічних апаратів

The aim of this work is to identify the features of expected cost estimation for R&amp;D’s on spacecraft development. The study is based on a methodological approach to expected cost estimation for R&amp;D’s on spacecraft development. The cost estimation model is based on a method of componentwise analogy for relatively simple spacecraft components, moving along the edges of a weighted oriented tree graph that models the spacecraft technical structure, and fuzzy mathematics methods. The methodological approach will allow one to obtain required R&amp;D expected cost indices early in the spacecraft development when the standardized cost estimation method and parametric methods are difficult to use because of the insufficiency of bug-free design and manufacture documentation and statistical data on labor intensiveness and materials consumption. The design novelty, R&amp;D complexity, and work automation coefficients are determined by converting the index value from a fuzzy number in a fuzzy interval into a crisp number, thus allowing one to reduce the effect of subjective factors. Calculating the engineering-and-economical indices of a spacecraft by all R&amp;D participants using the same methodological approach increases the accuracy and shortens the time of the computational process. Conducting the calculations in a systematic way will fill the statistical base of the space sector with labor intensiveness and materials consumption data needed for estimating the cost of new spacecraft and components thereof using a unified concept package – a glossary. The paper presents the operation sequence of estimating the cost of R&amp;D on spacecraft development and describes the required input data and the output data format.

Supersolvable saturated matroids and chordal graphs

A matroid is supersolvable if it has a maximal chain of flats, each of which is modular. A matroid is saturated if every round flat is modular. In this article we present supersolvable saturated matroids as analogues to chordal graphs, and we show that several results for chordal graphs hold in this matroidal context. In particular, we consider matroid analogues of the reduced clique graph and clique trees for chordal graphs. The latter is a maximum-weight spanning tree of the former. We also show that the matroid analogue of a clique tree is an optimal decomposition for the matroid parameter of tree-width.

Feedback vertex set reconfiguration in planar graphs

We study the complexity of deciding whether for two given feedback vertex sets of a graph there is a step-by-step transformation between them, such that for each feedback vertex set in the transformation, the next one is obtained by exchanging a single vertex. We give a classification of the complexity of this question for planar graphs in terms of the maximum degree. We show that for planar graphs of maximum degree at most three the problem is tractable because there always exists a transformation, while it is PSPACE-complete when the maximum degree is at most four. The positive side of the classification extends to K3,3-minor-free graphs of maximum degree three. We then consider the Matroid Parity problem, which generalizes feedback vertex sets in graphs of maximum degree three as well as matchings and spanning trees in general graphs. Generalizing known results for the latter two we show that there always exists a transformation between any two non-maximum independent parity sets.