Authors: Ghebleh, Mohammad
Kanso, Ali
Stevanović, Dragan 
Title: On trees with smallest resolvent energy
Journal: Match
Volume: 77
Issue: 3
First page: 635
Last page: 654
Issue Date: 1-Jan-2017
Rank: M21a
ISSN: 0340-6253
Abstract: 
Let Pn-1(a) be the tree obtained by attaching a pendent vertex at position a of the (n-1)-vertex path Pn-1. We prove here a conjecture of Gutman et al. [MATCH Commun. Math. Comput. Chem. 73 (2015), 267{270] that Pn-1(a) has the a-th smallest resolvent Estrada index among all trees of order n, for 2 ≤ a ≤ 〈n/2〉, and show that the analogous result also holds for the resolvent energy.
Publisher: Faculty of Sciences, University of Kragujevac
Project: Kuwait University, Research Grant No. SM10/15

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