The Zagreb indices of graphs with a given clique number

For a (molecular) graph, the first Zagreb index M 1 is equal to the sum of squares of the degrees of vertices, and the second Zagreb index M 2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Let W n , k be the set of connected n -vertex graphs with clique number k . In this work we characterize the graphs from W n , k with extremal (maximal and minimal) Zagreb indices, and determine the values of corresponding indices.