The inverse sum indeg index of graphs with some given parameters

Abstract

Let [Formula: see text] be a simple connected graph. The inverse sum indeg index of [Formula: see text], denoted by [Formula: see text], is defined as the sum of the weights [Formula: see text] of all edges [Formula: see text] of [Formula: see text], where [Formula: see text] denotes the degree of a vertex in [Formula: see text]. In this paper, we derive some bounds for the inverse sum indeg index in terms of some graph parameters, such as vertex (edge) connectivity, chromatic number, vertex bipartiteness, etc. The corresponding extremal graphs are characterized, respectively.