On the first reformulated Zagreb indices of graphs with a given clique number.

Milicevic et al. introduced the reformulated Zagreb indices, which is a natural generalization of classical Zagreb indices in chemical graph theory. Let W-n,W-k denote the family of connected graphs of order n with clique number k. In the paper, we first study some extremal properties of the first reformulated Zagreb index. Based on these properties, we give the sharp bounds of first reformulated Zagreb index of W-n,W-k, and characterize the corresponding extremal graphs with minimum and maximum first reformulated Zagreb indices, respectively.