Sharp bounds on general multiplicative Zagreb indices of trees

The first and second general multiplicative Zagreb indices of a simple graph are defined as the product over all pairs of adjacent vertices a, b of the terms d(a) + d(b) and d(a) d(b) , respectively, where d(a) denotes the degree of the vertexa, and is a real number.In this paper, we obtain bounds on these indices for trees with fixed maximum degree, and characterize the extremal cases.