A note on the modified albertson index

Abstract

The modified Albertson index, denoted by A*, of a graph G is defined as Ä(G) = ∑ ue ε (C) |(du)2 - (d2|) where du, dv denote the degrees of the vertices u, v, respectively, of G and E(G) is the edge set of G. In this note, a sharp lower bound of Ä in terms of the maximum degree for the case of trees is derived. The n-vertex trees having maximal and minimal A* values are also characterized here. Moreover, it is shown that A*(G) is a non-negative even integer for every graph G and that there exist infinitely many connected graphs whose A* value is 2t for every integer t € {0,3,4,5} U {8,9,10, • • •}. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.