The multiplicative Zagreb indices of graphs with given connectivity or number of pendant vertices

Abstract

For a graph $G$, the first multiplicative Zagreb index ${\prod }_1(G)$ is the product of squares of vertex degrees, and the second multiplicative Zagreb index ${\prod }_2(G)$ is the product of products of degrees of pairs of adjacent vertices. In this paper, we explore graphs with extremal ${\Pi }_1(G)$ and ${\Pi }_2(G)$ in terms of (edge) connectivity and pendant vertices. The corresponding extremal graphs are characterized with given connectivity at most $k$ and $p$ pendant vertices. In addition, the maximum and minimum values of ${\prod }_1(G)$ and ${\prod }_2(G)$ are provided. Our results extend and enrich some known conclusions.

arXiv admin note: substantial text overlap with arXiv:1704.06943