Results 11 to 20 of about 167 (150)
The nullity of bicyclic signed graphs [PDF]
Linear and Multilinear Algebra, 2013 Let Γbe a signed graph and let A(Γ) be the adjacency matrix of Γ. The nullity of Γis the multiplicity of eigenvalue zero in the spectrum of A(Γ). In this paper we characterize the signed graphs of order n with nullity n-2 or n-3, and introduce a graph transformation which preserves the nullity.
Fan, Yi-Zheng +2 more
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On the index of unbalanced signed bicyclic graphs [PDF]
Computational and Applied Mathematics, 2021 In this paper, we focus on the index ( largest eigenvalue) of the adjacency matrix of connected signed graphs. We give some general results on the index when the corresponding signed graph is perturbed. As applications, we determine the first five largest index among all unbalanced bicyclic graphs on n >= 36 vertices together with the corresponding ...
Changxiang He +3 more
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Ordering graphs with large eccentricity-based topological indices
Journal of Inequalities and Applications, 2021 For a connected graph, the first Zagreb eccentricity index ξ 1 $\xi _{1}$ is defined as the sum of the squares of the eccentricities of all vertices, and the second Zagreb eccentricity index ξ 2 $\xi _{2}$ is defined as the sum of the products of the ...
Yunfang Tang, Xuli Qi
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The Orderings of Bicyclic Graphs and Connected Graphs by Algebraic Connectivity [PDF]
The Electronic Journal of Combinatorics, 2010 The algebraic connectivity of a graph $G$ is the second smallest eigenvalue of its Laplacian matrix. Let $\mathscr{B}_n$ be the set of all bicyclic graphs of order $n$. In this paper, we determine the last four bicyclic graphs (according to their smallest algebraic connectivities) among all graphs in $\mathscr{B}_n$ when $n\geq 13$.
Jianxi Li, Ji-Ming Guo, Wai Chee Shiu
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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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Applied Mathematics Letters, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stefan Grünewald, Dragan Stevanovic
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Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance
Journal of Mathematics, 2021 Let G=V,E be a connected graph. The resistance distance between two vertices u and v in G, denoted by RGu,v, is the effective resistance between them if each edge of G is assumed to be a unit resistor.
Wenjie Ning, Kun Wang, Hassan Raza
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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 Minimum Generalized Degree Distance Index of Cyclic Graphs
International Journal of Mathematics and Mathematical Sciences, 2023 Topological index (TI) is a mapping that associates a real number to the under study (molecular) graph which predicts its various physical and chemical properties.
Nadia Khan +3 more
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On the inverse mostar index problem for molecular graphs [PDF]
Transactions on CombinatoricsMostar indices are recently proposed distance-based graph invariants, that already have been much investigated and found applications. In this paper, we investigate the inverse problem for Mostar indices of unicyclic and bicyclic molecular graphs.
Liju Alex, Ivan Gutman
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