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Extremal Bicyclic Graphs with Respect to Permanental Sums and Hosoya Indices
AxiomsGraph polynomials is one of the important research directions in mathematical chemistry. The coefficients of some graph polynomials, such as matching polynomial and permanental polynomial, are related to structural properties of graphs.
Tingzeng Wu, Yinggang Bai, Shoujun Xu
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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 the Signless Laplacian Spectral Radius of Bicyclic Graphs with Perfect Matchings [PDF]
The Scientific World Journal, 2014 The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined.
Jing-Ming Zhang +2 more
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Hosoya Indices of Bicyclic Graphs
Croatica Chemica Acta, 2009 Given a molecular graph G, the Hosoya index Z(G) of G is defined as the total number of the matchings of the graph. Let Bn denote the set of bicyclic graphs on n vertices. In this paper, the minimal, the second-, the third-, the fourth-, and the fifth-minimal Hosoya indices of bicyclic graphs in the set Bn are characterized.
Li, Shuchao, Li, Xuechao, Zhu, Zhongxun
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On bicyclic graphs with maximal energy
Linear Algebra and its Applications, 2007 The energy of a graph is the sum the absolute values of its eigenvalues. The main result of the article is the construction of the graph with maximal energy in the set of bicyclic graphs. This result gives a partial solution to Gutman's conjecture for molecular graphs with maximal energy.
Li, Xueliang, Zhang, Jianbin
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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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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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Signed bicyclic graphs with minimal index [PDF]
, 2023 The index of a signed graph \Sigma = (G; \sigma) is just the largest eigenvalue of its adjacency matrix. For any n > 4 we identify the signed graphs achieving the minimum index in the class of signed bicyclic graphs with n vertices.
Ciampella A., Brunetti M.
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Iota energy orderings of bicyclic signed digraphs [PDF]
Transactions on Combinatorics, 2021 The concept of energy of a signed digraph is extended to iota energy of a signed digraph. The energy of a signed digraph $S$ is defined by $E(S)=\sum_{k=1}^n|{Re}(z_k)|$, where ${Re}(z_k)$ is the real part of eigenvalue $z_k$ and $z_k$ is the ...
Xiuwen Yang, Ligong Wang
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