摘要:For a (molecular) graph G , the first and the second entire Zagreb indices are defined by the formulas M 1 ε G = ∑ x ∈ V G ∪ E G d x 2 and M 2 ε G = ∑ x is either adjacent or incident to y d x d y in which d x represents the degree of a vertex or an edge x . In the current manuscript, we establish some lower bounds on the first and the second entire Zagreb indices and determine the extremal trees which achieve these bounds.