Resolvent Energy of Unicyclic, Bicyclic and Tricyclic Graphs
Abstract: The resolvent energy of a graph G of order n is defined as ER(G) = ∑(n − λi)-1, where λ1, λ2, . . . , λn are the eigenvalues of G. In a recent work [Gutman et al., MATCH Commun. Math. Comput. Chem. 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.
engleski
2017
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Keywords: Graph spectrum, energy of graphs, resolvent energy