The Bounds for the First General Zagreb Index of a Graph

Authors : Rao Lİ

Pages : 132-135

Doi:10.32323/ujma.973671

View : 15 | Download : 10

Publication Date : 2021-12-30

Article Type : Research Paper

Abstract :The first general Zagreb index of a graph $G$ is defined as the sum of the $\alpha$th powers of the vertex degrees of $G$, where $\alpha$ is a real number such that $\alpha \neq 0$ and $\alpha \neq 1$. In this note, for $\alpha > 1$, we present upper bounds involving chromatic and clique numbers for the first general Zagreb index of a graph; for an integer $\alpha \geq 2$, we present a lower bound involving the independence number for the first general Zagreb index of a graph.
Keywords : The first general Zagreb index, The chromatic number, The clique number