On the maximum and minimum multiplicative Zagreb indices of graphs with given number of cut edges

2017/05/06 by Wang, Shaohui, Wang, Chunxiang, Chen, Lin
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.02482

Abstract

For a molecular graph, the first multiplicative Zagreb index Π₁ is equal to the product of the square of the degree of the vertices, while the second multiplicative Zagreb index Π₂ is equal to the product of the endvertex degree of each edge over all edges. Denote by \mathbbG_n,k the set of graphs with n vertices and k cut edges. In this paper, we explore graphs in terms of a number of cut edges. In addition, the maximum and minimum multiplicative Zagreb indices of graphs with given number of cut edges are provided. Furthermore, we characterize graphs with the largest and smallest Π₁(G) and Π₂(G) in \mathbbG_n,k, and our results extend and enrich some known conclusions.

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