INTEGER CORDIAL LABELING OF SOME STAR AND BISTAR RELATED GRAPHS

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 29

Abstract

An integer cordial labeling of a graph $G^{*}(p,q)$ is an injective map $g:V \rightarrow \displaystyle\left[\frac{-p}{2}, \ldots, \frac{p}{2}\right]^{*}$ or $\displaystyle\left[-\left\lfloor{\frac{p}{2}} \right\rfloor, \ldots,\left\lfloor{\frac{p}{2}} \right\rfloor \right]$ as $p$ is even or odd, which induces an edge labeling $g: E \rightarrow \{0,1\}$ defined by

\[g(uv)=\left\{\begin{array}{cl}

1,& g(u)+g(v) \geq 0\\

0,& \mbox{otherwise}\end{array}\right.\]

such that the number of edges labeled 1 and the number of edges labeled 0 differ by at most 1. If a graph has integer cordial labeling (I.C.L.), then it is called integer cordial graph (I.C.G.).

In this paper, we investigate the existence of integer cordial Labeling of Star and Bistar related graphs.

Keywords and Phrases

Integer Cordial Labeling, Integer Cordial Graph, Shadow graph, Splitting of a Graph, Degree Splitting of a Graph.

A.M.S. subject classification

05C78.

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