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Maximal elliptic Sombor index of bicyclic graphs [PDF]
Contributions to MathematicsLet G be a simple connected graph with edge set E ( G ) . The concept of the elliptic Sombor index ( ESO ) was recently introduced by Gutman, Furtula, and Oz in mathematical chemistry.
Fuxian Qi, Zhen Lin
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The Nullity of Bicyclic Signed Graphs [PDF]
Linear and Multilinear Algebra, 2012 Let \Gamma be a signed graph and let A(\Gamma) be the adjacency matrix of \Gamma. The nullity of \Gamma is the multiplicity of eigenvalue zero in the spectrum of A(\Gamma).
Cheng B +7 more
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Metric Dimensions of Bicyclic Graphs
Mathematics, 2023 The distance d(va,vb) between two vertices of a simple connected graph G is the length of the shortest path between va and vb. Vertices va,vb of G are considered to be resolved by a vertex v if d(va,v)≠d(vb,v).
Asad Khan +5 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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On the Extremal Weighted Mostar Index of Bicyclic Graphs [PDF]
AxiomsLet G be a simple connected graph with edge set E(G) and vertex set V(G). The weighted Mostar index of a graph G is defined as w+Mo(G)=∑e=uv∈E(G)(dG(u)+dG(v))|nu(e)−nv(e)|, where nu(e) denotes the number of vertices closer to u than to v for an edge uv ...
Yuwei He, Mengmeng Liu
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The Aα-spectral radius of complements of bicyclic and tricyclic graphs with n vertices [PDF]
Special Matrices, 2021 Recently, the extremal problem of the spectral radius in the class of complements of trees, unicyclic graphs, bicyclic graphs and tricyclic graphs had been studied widely.
Chen Chaohui +2 more
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Further Results on the Nullity of Signed Graphs [PDF]
Journal of Applied Mathematics, 2014 The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we apply the coefficient theorem on the characteristic polynomial of a signed graph and
Yu Liu, Lihua You
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On the Hosoya Indices of Bicyclic Graphs with Small Diameter [PDF]
Journal of Chemistry, 2021 Let G be a graph. The Hosoya index of G, denoted by zG, is defined as the total number of its matchings. The computation of zG is NP-Complete. Wagner and Gutman pointed out that it is difficult to obtain results of the maximum Hosoya index among tree ...
Tingzeng Wu, Yong Yu
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Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance [PDF]
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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Maximum values of sombor index of bicyclic graphs with a given matching number [PDF]
RAIRO - Theoretical Informatics and Applications, 2023 Sombor index is a popular vertex-degree-based topological index recently. In this paper, the maximum values of Sombor index for the class of all bicyclic graphs with a given matching number are wholly determined, then the extremal graphs with these ...
Chunlei Xu, Guanru Li
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