A note on Zagreb indices

Abstract

For a (molecular) graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. We provide upper bounds for the Zagreb indices M 1 and M2 of quadrangle-free graphs, in terms of the number of vertices and the number of edges, and determine the graphs for which the bounds are attained.