Chromatic Number to the Transformation $(G^{---})$ of $K_n$, $W_n$ and $F_n$

Abstract

Let $G=(V,E)$ be an undirected simple graph. The transformation graph $G^{---}$ of G is a simple graph with vertex set $V(G)\cup E(G)$ in which adjacency is defined as follows: (a) two elements in $V(G)$ are adjacent if and only if they are non-adjacent in $G,$ (b) two elements in $E(G)$ are adjacent if and only if they are non-adjacent in $G,$ and (c) an element of $V(G)$ and an element of $E(G)$ are adjacent if and only if they are non-incident in $G$. In this paper, we determine the chromatic number of Transformation graph $G^{---}$ for Complete, Wheel and Friendship graph.