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Wang, Wen-Huan; Xu, Wei-Wei

Graphs with the maximal Estrada indices. (English) Zbl 1292.05181

Linear Algebra Appl. 446, 314-328 (2014).
Summary: Two new transformations are proposed to compare the Estrada indices between two graphs. Let \({\Psi}_{n,m}\) be the set of the \((n,m)\)-graphs, where \(n\) and \(m\) are the numbers of vertices and edges, respectively. The graphs with the maximal Estrada indices in \({\Psi}_{n,m}\) are deduced by the new method for three cases, namely unicyclic and bipartite unicyclic graphs \((m=n)\), bicyclic graphs \((m=n+1)\), and the \((n,m)\)-graphs without even cycles \((n+1 \leqslant m\leqslant 3(n-1)/2)\).

Cited in 10 Documents

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C35 Extremal problems in graph theory

Keywords:

\((n, m)\)-graph; Estrada index; transformation
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\textit{W.-H. Wang} and \textit{W.-W. Xu}, Linear Algebra Appl. 446, 314--328 (2014; Zbl 1292.05181)
Full Text: DOI

References:

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