On extremal multiplicative Zagreb indices of trees with given domination number

Abstract For a (molecular) graph, the first multiplicative Zagreb index Π 1 is equal to the product of squares of the vertex degrees, and the second multiplicative Zagreb index Π 2 is equal to the product of the products of degrees of pairs of adjacent vertices. In this paper, we explore the multiplicative Zagreb indices in terms of domination number. Sharp upper and lower bounds of Π 1 and Π 2 are given. In addition, the corresponding extreme graphs are characterized, and our conclusions enrich and extend some known results.