Extremal Zagreb Indices of Graphs with a Given Number of Cut Edges

Abstract

For a graph, the first Zagreb index M 1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M 2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Denote by Gn,k the set of graphs with n vertices and k cut edges. In this paper, we showed the types of graphs with the largest and the second largest M 1 and M 2 among Gn,k. © 2012 The Author(s).