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

For a (molecular) graph, the first Zagreb index M 1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M 2 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 n with κ ( G ) ≤ k (resp. κ ′ ( G ) ≤ k ) and sharp lower and upper bounds are obtained for M 1 ( G ) and M 2 ( G ) for G ∈ V n k (resp. E n k ), where V n k is the set of graphs of order n with κ ( G ) ≤ k ≤ n − 1 , and E n k is the set of graphs of order n with κ ′ ( G ) ≤ k ≤ n − 1 .