On extremal multiplicative Zagreb indices of trees with given domination number

摘要

For a (molecular) graph, the first multiplicative Zagreb index Π1 is equal to the product of squares of the vertex degrees, and the second multiplicative Zagreb index Π2 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 Π1 and Π2 are given. In addition, the corresponding extreme graphs are characterized, and our conclusions enrich and extend some known results.