Maxima of the [formula omitted]-index of graphs with given size and domination number.

The A α -matrix of a graph G was defined by Nikiforov in 2017 as A α (G) = α D (G) + (1 − α) A (G) , where α ∈ [ 0 , 1 ] , D (G) and A (G) are the diagonal matrix of degrees and the adjacency matrix respectively. The largest eigenvalue of A α (G) is called A α -index of G. In this paper, we completely determine the extremal graphs with maximal A α -index among all graphs with size m , domination number γ and no isolated vertices for α ∈ [ 1 2 , 1). [ABSTRACT FROM AUTHOR]