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The multiplicative Zagreb co-indices on two graph operators

Mansoureh Deldar, Mehdi Alaeiyan

Department of Mathematics, Karaj Branch, Islamic Azad University Karaj, Iran

Abstract: Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The first and second multiplicative Zagreb co-indices are defined as:
$$\overline\prod_1(G)=\prod_{uv\notin E(G)}[d_G(u)+d_G(v)],\quad\overline\prod_2(G)=\prod_{uv\notin E(G)}[d_G(u)d_G(v)], $$
respectively, where $d_G(u)$ is the degree of the vertex $u$ of $G$. The aim of this paper is to investigate the multiplicative Zagreb co-indices of the subdivision graphs of tadpole graphs and wheel graphs.

Keywords and phrases: multiplicative Zagreb co-indices, subdivision graph, Zagreb indices.

MSC: 05C05, 05C07, 05C90, 05C020

Received: 24.12.2014

Language: English