Extremal trees with respect to the first and second reformulated Zagreb index
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DOI:
https://doi.org/10.26637/mjm503/006Abstract
Let $G$ be a graph with edge set $E(G)$. The first and second reformulated Zagreb indices of $G$ are defined as $E M_1(G)=\sum_{e \in E(G)} \operatorname{deg}(e)^2$ and $E M_2(G)=\sum_{e \sim f} \operatorname{deg}(e) \operatorname{deg}(f)$,respectively, where $\operatorname{deg}(e)$ 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 operationMathematics Subject Classification:
Mathematics- Pages: 524-530
- Date Published: 01-07-2017
- Vol. 5 No. 03 (2017): Malaya Journal of Matematik (MJM)
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- The research of the authors are partially supported by the University of Kashan under grant no 572760/3.
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