On the sharp upper and lower bounds of multiplicative Zagreb indices of graphs with connectivity at most k

Abstract

For a (molecular) graph, the first multiplicative Zagreb index ${\prod }_1(G)$ is the product of the square of every vertex degree, and the second multiplicative Zagreb index ${\prod }_2(G)$ 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 ${\prod }_1(G)$ and ${\prod }_2(G)$ 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.