Group ${1, -1, i, -i}$ Cordial Labeling of sum of $C_n$ and $K_m$ for some $m$

Abstract

Let G be a (p,q) graph and A be a group. We denote the order of an element $a in A $ by $o(a).$ Let $ f:V(G)rightarrow A$ be a function. For each edge $uv$ assign the label 1 if $(o(f(u)),o(f(v)))=1 $or $0$ otherwise. $f$ is called a group A Cordial labeling if $|v_f(a)-v_f(b)| leq 1$ and $|e_f(0)- e_f(1)|leq 1$, where $v_f(x)$ and $e_f(n)$ respectively denote the number of vertices labelled with an element $x$ and number of edges labelled with $n (n=0,1).$ A graph which admits a group A Cordial labeling is called a group A Cordial graph. In this paper we define group ${1 ,-1 ,i ,-i}$ Cordial graphs and characterize the graphs $C_n + K_m (2 leq m leq 5)$ that are group ${1 ,-1 ,i ,-i}$ Cordial.