Results 121 to 130 of about 167 (150)

On the spectral moment of quasi-bicyclic graphs

Applied Mathematics and Computation, 2019
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Longfei Fang, Bing Wang, Mingqing Zhai
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ON THE NULL-SPACES OF BICYCLIC SINGULAR GRAPHS

Discrete Mathematics, Algorithms and Applications, 2011
In [M. Nath and B. K. Sarma, On the null-spaces of unicyclic and acyclic graphs, Linear Algebra Appl.427 (2007) 42–54], Nath and Sarma gave an algorithm to find a basis for the null-space of a graph G when G is singular acyclic or unicyclic. In this paper, we find a basis for the null-space of G when G is a bicyclic singular graph.
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Computing the Scattering Number of Bicyclic Graphs

2010 International Conference on Computational Intelligence and Security, 2010
The scattering number of a noncomplete connected graph $G$ is defined by $s(G)=\max\{\omega(G-X)-|X|:X\subset V(G), \omega(G-X)\ge 2\}$, where $\omega(G-X)$ denotes the number of components of $G-X$. This parameter can be used to measure the vulnerability of networks.
Bing Chen 0006, Shenggui Zhang
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On Sombor Index of Unicyclic and Bicyclic Graphs

Journal of Interconnection Networks
Gutman proposed a topological index called the Sombor index, which was defined as [Formula: see text] where [Formula: see text] is the degree of the vertex [Formula: see text] in graph [Formula: see text]. In this paper, we determine the second-minimum and second-maximum values of the Sombor index over all the unicyclic graphs of order [Formula: see ...
Huan Tan, Biao Zhao
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On bicyclic graphs with minimal energies

Journal of Mathematical Chemistry, 2005
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Zhang, Jianbin, Zhou, Bo
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Bicyclic Graphs with Nullity n−5

2013
Let \( G \) be a simple undirected graph on n vertices, \( A(G) \) be its adjacency matrix. The nullity \( \eta (G) \) of the graph \( G \) is the multiplicity of the eigenvalue zero in its spectrum. In this paper, we characterize the bicyclic graphs with nullity \( n - 5 \).
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Bicyclic graphs with minimum energy

Linear and Multilinear Algebra, 2001
If λ1, λ2,…,λn are the eigenvalues of a graph G, then the energy of this graph is denned as . For n⩾6, let be the graph obtained by joining n−5 pendant vertices to a vertex of degree three of the complete bipartite graph K 2. We show that for all values of n⩾6, S 4,4 n has the minimal energy among all n vertex connected bicyclic graphs with at most one
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Minimal configuration bicyclic graphs

Linear and Multilinear Algebra, 2012
The nullity η(G) of a graph G is the multiplicity of zero as an eigenvalue of the adjacency matrix of G. If η(G) = 1, then the core of G is the subgraph induced by the vertices associated with the nonzero entries of the kernel eigenvector. The set of vertices which are not in the core is the periphery of G.
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Extremal Arithmetic–Geometric Index of Bicyclic Graphs

Circuits, Systems, and Signal Processing, 2023
Baohua Niu, Shuming Zhou, Hong Zhang 0044   +2 more
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Unicyclic and bicyclic graphs with maximum exponential second Zagreb index

Discrete Applied Mathematics, 2022
Mehdi Eliasi
exaly