Comparing the Zagreb Indices

Hansen, Pierre; Vukicevic, Damir

Let $G=(V,E)$ be a simple graph with $n=|V|$ vertices and $m=|E|$ edges; let $d_1, d_2,\ldots, d_n$ denote the degrees of the vertices of $G$ . If $\Delta=\max_i d_i\leq 4, G$ is a chemical graph. The first and second Zagreb indices are defined as

$M_1=\sum\limits_{i\in V} d^2_i$ and $M_2=\quad \sum\limits_{(i,j)\in E}\quad d_i d_j$ .

We show that for all chemical graphs $M_1/n \leq M_2/m$ . This does not hold for all general graphs, connected or not.

Published September 2006 , 12 pages

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G-2006-51

Comparing the Zagreb Indices

Pierre Hansen and Damir Vukicevic

Research Axis

Research applications

Document