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## The multiplicative Zagreb co-indices on two graph operators

Authors: Mansoureh Deldar, Mehdi Alaeiyan

### 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: $${\overline{\prod}}_1(G)={\prod}_{uv\notin E(G)}[d_G(u)+d_G(v)]~,~{\overline{\prod}}_2(G)={\prod}_{uv\notin E(G)}[d_G(u)d_G(v)],$$ 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

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