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arXiv · 1512.08938

Resolvent Energy of Unicyclic, Bicyclic and Tricyclic Graphs

Luiz Emilio Allem·Juliane Capaverde·Vilmar Trevisan·Ivan Gutman·Emir Zogić·Edin Glogić
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Abstract

The resolvent energy of a graph $G$ of order $n$ is defined as $ER=\sum_{i=1}^n (n-λ_i)^{-1}$, where $λ_1,λ_2,\ldots,λ_n$ are the eigenvalues of $G$. In a recent work [Gutman et al., {\it MATCH Commun. Math. Comput. Chem.\/} {\bf 75} (2016) 279--290] the structure of the graphs extremal w.r.t. $ER$ were conjectured, based on an extensive computer--aided search. We now confirm the validity of some of these conjectures.

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Luiz Emilio Allem, Juliane Capaverde, Vilmar Trevisan, Ivan Gutman, Emir Zogić, Edin Glogić. 2015-12-30. Resolvent Energy of Unicyclic, Bicyclic and Tricyclic Graphs. https://arxiv.org/abs/1512.08938

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