Extremal trees with respect to the first and second reformulated Zagreb index

Extremal trees with respect to the first and second reformulated Zagreb index

**Authors : **

Ali Ghalavand and Ali Reza Ashrafi *

**Author Address : **

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317 − 51116, I. R. Iran.

**Abstract : **

Let $G$ be a graph with edge set $E(G)$. The first and second reformulated Zagreb indices of $G$ are defined as $EM_1(G) = sum_{ein E(G)}deg(e)^2$ and $EM_2(G) = sum_{e sim f}deg(e)deg(f)$,respectively, where $deg(e)$ denotes the degree of the edge $e$, and $e sim f$ means that the edges $e$ and $f$ are incident. In this paper, the extremal trees with respect to the first and second reformulated Zagreb indices are presented.

**Keywords : **

Tree, first reformulated Zagreb, second reformulated Zagreb, graph operation.

**DOI : **

**Article Info : **

*Received : * October 11, 2016; *Accepted : * April 23, 2017.