Results 11 to 20 of about 2,717 (193)
Unicyclic Components in Random Graphs [PDF]
Journal of Physics A: Mathematical and General, 2004 The distribution of unicyclic components in a random graph is obtained analytically. The number of unicyclic components of a given size approaches a self-similar form in the vicinity of the gelation transition.
Aldous D J +25 more
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Unicyclic Graphs with equal Laplacian Energy [PDF]
Linear and Multilinear Algebra, 2013 We introduce a new operation on a class of graphs with the property that the Laplacian eigenvalues of the input and output graphs are related. Based on this operation, we obtain a family of order (square root of n) noncospectral unicyclic graphs on n ...
Fritscher, Eliseu +2 more
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The Extremal Unicyclic Graphs With Given Girth for Exponential VDB Topological Indices
Journal of MathematicsTopological indices are widely used molecular structure descriptors in chemistry and pharmaceutics, which help analyze and predict the physicochemical properties and biological activity of compounds.
Zhenhua Su, Zikai Tang
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On the least signless Laplacian eigenvalue of a non-bipartite connected graph with fixed maximum degree [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we determine the unique graph whose least signless Laplacian eigenvalue attains the minimum among all non-bipartite unicyclic graphs of order n with maximum degree Δ and among all non-bipartite connected graphs of order n with maximum ...
Shu-Guang Guo, Rong Zhang
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On the Core of a Unicyclic Graph
Ars Mathematica Contemporanea, 2011 A set S is independent in a graph G if no two vertices from S are adjacent. By core(G) we mean the intersection of all maximum independent sets. The independence number alpha(G) is the cardinality of a maximum independent set, while mu(G) is the size of ...
Levit, Vadim E., Mandrescu, Eugen
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On the Maximum SC Index of Chemical Unicyclic Graphs
Journal of MathematicsThe sum-connectivity SC index of a graph G is defined as SCG=∑μν∈EG1/Θμ+Θν, where Θμ denotes the vertex degree of μ in G. In this paper, the fourth largest value of SC index for the chemical unicyclic graphs of order n≥7 is determined.
Hui-Yan Cheng, Lei Chen, Sattar Alyar
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Burning Numbers of t-unicyclic Graphs [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2021 Given a graph $G$, the burning number of $G$ is the smallest integer $k$ for which there are vertices $x_1, x_2,\ldots,x_k$ such that $(x_1,x_2,\ldots,x_k)$ is a burning sequence of $G$. It has been shown that the graph burning problem is NP-complete, even for trees with maximum degree three, or linear forests. A $t$-unicyclic graph is a unicycle graph
Ruiting Zhang, Yingying Yu, Huiqing Liu
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Null decomposition of unicyclic graphs [PDF]
Discrete Applied Mathematics, 2020 arXiv admin note: text overlap with arXiv:1907 ...
L. Emilio Allem +4 more
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Incidence and Laplacian matrices of wheel graphs and their inverses
The American Journal of Combinatorics, 2023 It has been an open problem to find the Moore-Penrose inverses of the incidence, Laplacian, and signless Laplacian matrices of families of graphs except trees and unicyclic graphs.
Jerad Ipsen, Sudipta Mallik
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The Signless Laplacian Estrada Index of Unicyclic Graphs [PDF]
Mathematics Interdisciplinary Research, 2017 For a simple graph G, the signless Laplacian Estrada index is defined as SLEE(G)=∑ni=1eqi, where q1, q2,..., qn are the eigenvalues of the signless Laplacian matrix of G.
Hamid Reza Ellahi +3 more
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