Twig and Cycle Related Near Mean Cordial Graphs

Abstract

Let $G = (V, E)$ be a simple graph. A Near Mean Cordial Labeling of G is a function in $f : V(G) \to \{1, 2, 3,\dots, p-1, p+1\}$ such that the induced map f* defined by \[ f^*(uv) = \left\{ \begin{array}{ll} 1, & \hbox{if $\left(f\left(u\right)+f\left(v\right)\right)\equiv 0\ (mod\;2)$;} \\ 0, & \hbox{else.} \end{array} \right. \] and it satisfies the condition $|e_f(0)-e_f(1)|\le 1$, where $e_f(0)$ and $e_f(1)$ represent the number of edges labeled with 0 and 1 respectively. A graph is called a Near Mean Cordial Graph if it admits a near mean cordial labeling. In this paper, it is to be proved that $Twig\ T(n)$, $\langle C_n : C_{n-1}\rangle$ and $W_n$ (When $n \equiv 0,2,3\ (mod\ 4)$) are Near Mean Cordial graphs. Also, $W_n$ (When $n \equiv 1\ (mod\ 4)$) are not Near Mean Cordial graphs.