Sharp bounds for the modified multiplicative Zagreb indices of graphs with vertex connectivity at most k

Abstract

For a (molecular) graph, the first multiplicative Zagreb index 1 (G) is the product of the square of every vertex degree, and the second multiplicative Zagreb index 2 (G) is the product of the products of degrees of pairs of adjacent vertices. In this paper, we explore graphs in terms of (edge) connectivity. The maximum and minimum values of 1 (G) and 2 (G) of graphs with connectivity at most k are provided. In addition, the corresponding extremal graphs are characterized, and our results extend and enrich some known conclusions.