Isomorphisms of generalized Cayley graphs

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