On extremal Zagreb indices of trees with given domination number

Abstract

© 2016 Elsevier Inc. All rights reserved. First (M1) and second (M2) Zagreb indices are graph invariants that originate from chemical researches on total π-electron energy of conjugated molecules. There is a legion of articles dealing with these two indices. This paper presents upper bounds on Zagreb indices of trees in terms of domination number. These are strict bounds, and extremal trees are characterized. In addition, a lower bound for the first Zagreb index of trees with a given domination number is determined and the extremal trees are characterized as well. Finally, using previously known upper bound for Harary index (H) in terms of M1 and M2, a unique tree with given domination number that maximizes H is characterized.