Some Results on Contra Harmonic Cordial mean Graphs

Abstract

Let $f$ be a map from the vertex set $V(G)$ to $\{0, 1, 2\}$. For each edge $uv$ assign the label \[ \displaystyle \left\lceil\frac{(f(u))^2+(f(v))^2}{f(u)+f(v)}\right\rceil.\] Then $f$ is called a contra harmonic cordial  mean labeling if $|v_f (i)-v_f (j)|\leq1$ and $|e_f (i)-e_f (j)|\leq1$ for all $i,j\in {0,1,2}$  where $v_f (x)$ and $e_f (x)$ denote the number of vertices and edges respectively labeled with $x=0, 1,2.$ A graph with a contra harmonic cordial mean labeling is called a contra harmonic cordial mean graph. In this paper we investigate contra harmonic cardial mean labeling behavior of path, cycles, triangular snake, complete graphs and some more standard graphs.