, Volume 30, Issue 1, pp 109-118,
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Date: 15 Nov 2012

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


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 \({\mathcal{G}_{n,k}}\) 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 \({\mathcal{G}_{n,k}}\) .