On the maximum and minimum Zagreb indices of graphs with connectivity at most kk

For a (molecular) graph, the first Zagreb index M1M1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M2M2 is equal to the sum of the products of degrees of pairs of adjacent vertices. In this paper, we study the Zagreb indices of graphs of order nn with κ(G)≤kκ(G)≤k (resp. κ′(G)≤kκ′(G)≤k) and sharp lower and upper bounds are obtained for M1(G)M1(G) and M2(G)M2(G) for G∈Vnk (resp. Enk), where Vnk is the set of graphs of order nn with κ(G)≤k≤n−1κ(G)≤k≤n−1, and Enk is the set of graphs of order nn with κ′(G)≤k≤n−1κ′(G)≤k≤n−1.