Extremal values of two multiplicative type topological indices

The multiplicative-type topological index of a graph is defined as the product of a symmetric function of the degrees of all adjacent vertices. It can be regarded as the multiplicative version of the vertex-degree-based topological index of the graph. Based on some graph operations, the extremal values of the multiplicative sum Zagreb index for trees with at most three branch vertices are determined. Some upper bounds of the multiplicative sum Zagreb index in relation to graph parameters are also provided. Furthermore, the extremal values of the multiplicative Sombor index for chemical graphs and chemical trees are completely characterized, respectively.