Results 81 to 90 of about 828 (207)
The largest eigenvalue of unicyclic graphs
Discrete Mathematics, 2007 The author shows that the largest eigenvalue of the adjacency matrix of a unicyclic graph with the maximum vertex degree \(\Delta\) is bounded from above by \(2\sqrt{\Delta-1}\), while the largest eigenvalue of its Laplacian matrix is bounded by \(\Delta+2\sqrt{\Delta-1}\), with equality in the first case holding for all cycles, and in the second case ...
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The Moran Process on a Random Graph
Random Structures &Algorithms, Volume 66, Issue 3, May 2025.ABSTRACT We study the fixation probability for two versions of the Moran process on the random graph Gn,p$$ {G}_{n,p} $$ at the threshold for connectivity. The Moran process models the spread of a mutant population in a network. Throughout the process, there are vertices of two types, mutants, and non‐mutants.
Alan Frieze, Wesley Pegden
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On 2-power unicyclic cubic graphs
Electronic Journal of Graph Theory and Applications, 2022 Summary: In a graph, a cycle whose length is a power of two (that is, \(2^k\)) is called a 2-power cycle. In this paper, we show that the existence of an infinite family of cubic graphs which contain only one cycle whose length is a power of 2. Such graphs are called as 2-power unicyclic cubic graphs. Further we observe that the only 2-power cycle in a
Shariefuddin Pirzada +2 more
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Selection of an Optimal Warehouses Using Global Regular Domination in Graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.Let G = (V, E) be a simple graph. A subset S of V (G) is said to be global dominating set if S is a dominating set of the given graph G and its complement G. A subset whose induced subgraph is regular in G is also regular in G. A dominating set D of V (G) is called a regular dominating set if hSi is regular. In this article, we introduce global regular
R. Sundareswaran +6 more
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Computing the vertex separation of unicyclic graphs
Information and Computation, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
John A. Ellis, Minko Markov
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Stress in Directed Graphs: A Generalization of Graph Stress
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.In graph theory, centrality measures are used to identify the most important or influential nodes within a network. Stress centrality is one such measure, which helps quantify how “stressed” a node is within the overall graph structure based on the number of shortest paths that pass through it. Stress centrality provides a more thorough assessment of a
K. V. Madhumitha +4 more
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On General Sum‐Connectivity Index and Number of Segments of Fixed‐Order Chemical Trees
Journal of Mathematics, Volume 2025, Issue 1, 2025.Nowadays, one of the most active areas in mathematical chemistry is the study of the mathematical characteristics associated with molecular descriptors. The primary objective of the current study is to find the largest value of χα of graphs in the class of all fixed‐order chemical trees with a particular number of segments for α > 1, where χα is the ...
Muzamil Hanif +5 more
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On the signless Laplacian coefficients of unicyclic graphs
, 2013 Let G be a graph of order n and let View the MathML source be the characteristic polynomial of the signless Laplacian of G. Let Eg,n (respectively, Cg(Sn−g+1)) denote the unicyclic graph of order n obtained by a coalescence of a vertex in the cycle Cg ...
譚必信 +2 more
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A note on the minimum reduced reciprocal Randic index of n-vertex unicyclic graphs
Kuwait Journal of Science, 2017 Recent studies show that the reduced reciprocal Randi? (RRR) index possesses the second-best correlating ability amongthe several well known topological indices.
Akbar Ali, Akhlaq A. Bhatti
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The Entropy of Weighted Graphs with Atomic Bond Connectivity Edge Weights
Discrete Dynamics in Nature and Society, 2018 The aim of this report to solve the open problem suggested by Chen et al. We study the graph entropy with ABC edge weights and present bounds of it for connected graphs, regular graphs, complete bipartite graphs, chemical graphs, tree, unicyclic graphs ...
Young Chel Kwun +4 more
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