On general Zagreb indices over the matching edges of graphs

  • E. Suresh
  • V. Balaji
  • S. Sudhakar

Abstract

The first and second general Zagreb indices of a graph $G,$ with vertex set $V$ and edge set $E,$ are defined as $M_1^k(G) = \sum\nolimits_{v \in V} {d{{(v)}^k}} $ and $M_2^k(G) = \sum\nolimits_{uv \in E} {{{\left[ {d(u)d(v)} \right]}^k}} .$ For $M$ be any matching of size $k$, the first and second Zagreb indices over the matching edges are $M_1^2(M)$ and $M_2^1(M),$ respectively. In this paper, we present combinatorial identities relating $M_1^2(M)$ and $M_2^1(M).$ In addition, we give some new lower bounds for the first Zagreb index.

Published
2016-11-30
Section
Articles