### 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.

**How to Cite this Article:**Karthik Chidambaram, Group {1,−1,i,−i} cordial labeling of sum of Pn and Kn, J. Math. Comput. Sci., 7 (2017), 335-346 Copyright © 2017 Karthik Chidambaram. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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