Results 171 to 180 of about 1,782 (193)

On extremal bipartite bicyclic graphs

Journal of Mathematical Analysis and Applications, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shuchao Li
exaly   +2 more sources

Computing the Determinant of the Distance Matrix of a Bicyclic Graph

Electronic Notes in Theoretical Computer Science, 2019
Abstract Let G be a connected graph with vertex set V = {v1, ..., vn}. The distance d(vi, vj) between two vertices vi and vj is the number of edges of a shortest path linking them. The distance matrix of G is the n × n matrix such that its (i, j)-entry is equal to d(vi, vj).
Martin Dario Safe, Renata Del-Vecchio, Luciano Grippo   +2 more
exaly   +3 more sources

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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.
openaire   +1 more source

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 bicyclic graphs with minimal energies

Journal of Mathematical Chemistry, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bo Zhou
exaly   +3 more sources

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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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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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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Bicyclic oriented graphs with skew-rank 6

Applied Mathematics and Computation, 2015
Ligong Wang, Qiannan Zhou
exaly