The Zagreb indices of graphs with a given clique number

For a (molecular) graph, the first Zagreb index M1M1 is equal to the sum of squares of the degrees of vertices, and the second Zagreb index M2M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Let Wn,kWn,k be the set of connected nn-vertex graphs with clique number kk. In this work we characterize the graphs from Wn,kWn,k with extremal (maximal and minimal) Zagreb indices, and determine the values of corresponding indices.