# Comparing Zagreb indices and variable Zagreb indices

## Damir Vukicevic – University of Split, Croatia

Let `\(G=(V,E)\)`

be a simple graph with `\(n=|V|\)`

vertices and `\(m=|E|\)`

edges; let `\(d_1, d_2, \dots, d_n\)`

denote the degrees of the vertices of `\(G\)`

. If `\(\Delta=\max\limits_i d_i \leq 4\)`

, `\(G\)`

is a chemical graph.
The first and second Zagreb indices are defined as

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

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.