Results 11 to 20 of about 1,442 (223)
The first Dirichlet eigenvalue of bicyclic graphs [PDF]
Czechoslovak Mathematical Journal, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Guang-Jun, Zhang, Xiao-Dong
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Applied Mathematics Letters, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stefan Grünewald, Dragan Stevanovic
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Discrete Mathematics, 2008 Let \(\lambda_2\) be the second largest eigenvalue of the adjacency matrix of a graph. Graphs having \(\lambda_2\leq 2\) are called reflexive graphs. Since this property is hereditary, these graphs may be represented through sets of maximal graphs. In this paper, authors continue their previous line of study and construct maximal bicyclic reflexive ...
Zoran Radosavljevic +2 more
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Regularity of bicyclic graphs and their powers [PDF]
Journal of Algebra and Its Applications, 2019 Let [Formula: see text] be the edge ideal of a bicyclic graph [Formula: see text] with a dumbbell as the base graph. In this paper, we characterize the Castelnuovo–Mumford regularity of [Formula: see text] in terms of the induced matching number of [Formula: see text]. For the base case of this family of graphs, i.e.
Cid-Ruiz, Yairon +3 more
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On the nullity of bicyclic graphs
Linear Algebra and its Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hu, Shengbiao +2 more
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Unicyclic graphs with bicyclic inverses [PDF]
Czechoslovak Mathematical Journal, 2017 A graph is nonsingular if its adjacency matrix A(G) is nonsingular. The inverse of a nonsingular graph G is a graph whose adjacency matrix is similar to A(G)−1 via a particular type of similarity. Let H denote the class of connected bipartite graphs with unique perfect matchings.
Panda, Swarup Kumar
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Bicyclic graphs with maximum sum of the two largest Laplacian eigenvalues
Journal of Inequalities and Applications, 2016 Let G be a simple connected graph and S 2 ( G ) $S_{2}(G)$ be the sum of the two largest Laplacian eigenvalues of G. In this paper, we determine the bicyclic graph with maximum S 2 ( G ) $S_{2}(G)$ among all bicyclic graphs of order n, which confirms the
Yirong Zheng +3 more
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On the Laplacian coefficients of bicyclic graphs
Discrete Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chang-Xiang He, Hai-Ying Shan
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The Electronic Journal of Linear Algebra, 2017 A graph G is said to be nonsingular (resp., singular) if its adjacency matrix A(G) is nonsingular (resp., singular). The inverse of a nonsingular graph G is the unique weighted graph whose adjacency matrix is similar to the inverse of the adjacency matrix A(G) via a diagonal matrix of ±1s.
SWARUP PANDA +2 more
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On minimum algebraic connectivity of graphs whose complements are bicyclic
Open Mathematics, 2019 The second smallest eigenvalue of the Laplacian matrix of a graph (network) is called its algebraic connectivity which is used to diagnose Alzheimer’s disease, distinguish the group differences, measure the robustness, construct multiplex model ...
Liu Jia-Bao +3 more
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