# Vertex Switching in 3-Product Cordial Graphs

Document Type : Research Paper

Authors

2 Department of Mathematics, Kamaraj College of Engineering and Technology, Virudhunagar, India.

3 Department of Mathematics, Dr.G.U. Pope College of Engineering, Sawyerpuram,Thoothukudi District, Tamil Nadu, India

Abstract

A mapping  $f: V(G)\rightarrow\left\{0, 1, 2 \right\}$ is called 3-product cordial labeling if $\vert v_f(i)-v_f(j)\vert \leq 1$ and $\vert e_f(i)-e_f(j)\vert \leq 1$ for any $i, j\in \{0, 1, 2\}$, where $v_f(i)$ denotes the number of vertices labeled  with $i, e_f (i)$ denotes the number of edges $xy$ with $f(x)f(y)\equiv i(mod \ 3)$. A graph with  3-product cordial labeling is called  3-product cordial graph. In this paper we establish that vertex switching of wheel,gear graph and degree splitting of bistar are 3-product cordial graphs.