On Integer Cordial Labeling of Some Families of Graphs

Abstract

An integer cordial labeling of a graph $G(p,q)$ is an injective map $f:V\rightarrow [-\frac{p}{2}...\frac{p}{2}]^*$ or $[-\lfloor{\frac{p}{2}\rfloor}...\lfloor{\frac{p}{2}\rfloor}]$ as $p$ is even or odd, which induces an edge labeling $f^*: E \rightarrow \{0,1\}$ defined by $f^*(uv)=$ $\begin{cases} 1, f(u)+f(v)\geq 0\\ 0,\hspace{0.1 cm}\text{otherwise} \end{cases}$ such that the number of edges labelled with 1 and the number of edges labelled with 0 differ at most by 1. If a graph has integer cordial labeling, then it is called integer cordial graph. In this paper, we have proved that the Banana tree, $K_{1,n} \ast K_{1,m}$, Olive tree, Jewel graph, Jahangir graph, Crown graph admits integer cordial labeling.

Keywords

• banana tree
• olive tree
• jewel graph
• jahangir graph
• integer cordial labeling