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 \({\mathcal{G}_{n,k}}\) 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 \({\mathcal{G}_{n,k}}\).
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Chen, S., Liu, W. Extremal Zagreb Indices of Graphs with a Given Number of Cut Edges. Graphs and Combinatorics 30, 109–118 (2014). https://doi.org/10.1007/s00373-012-1258-8
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DOI: https://doi.org/10.1007/s00373-012-1258-8