Group {1,−1,i,−i} cordial labeling of sum of Pn and Kn

Abstract

Let G be a (p,q) graph and A be a group. For $a \in A$, we denote the order of $a$ by $o(a)$. Let $ f:V(G)\rightarrow A$ be a function. For each edge $uv$ assign the label 1 if $(o(u),o(v))=1 $or $0$ otherwise. $f$ is called a group A Cordial labeling if $|v_f(a)-v_f(b)| \leq 1$, $\forall a,b \in A$ 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 prove that $P_n + K_2$ is group $\{1 ,-1 ,i ,-i\}$ Cordial for every $n$. We further characterize $P_n + K_3, P_n + K_4 $ and $P_n + K_n ( n \leq 30)$ that are group $\{1 ,-1 ,i ,-i\}$ Cordial.