Resolvent Energy of Unicyclic, Bicyclic and Tricyclic Graphs
Allem, Luiz Emilio · Capaverde, Juliane · Trevisan, Vilmar · Gutman, Ivan · Zogić, Emir · Glogić, Edin
Original · EN
The resolvent energy of a graph G of order n is defined as ER=∑ᵢ₌₁ⁿ (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.
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