Edge Graceful Irregularity Strength of Wheel Related Graphs

Abstract

For a simple graph \textit{G}, the edge graceful irregular \textit{s-}labeling is a mapping $f:V\bigcup E\to \left\{1,2,3,\ldots ,s\right\}$ such that if for any two distinct edges \textit{e } and \textit{ g}, $wt\left(e\right)\ne wt\left(g\right)$, $wt\left(uv\right)=\left|f\left(u\right)+f\left(v\right)-f\left(uv\right)\right|$. The edge graceful irregularity strength of \textit{G}, denoted by $egs\left(G\right)$ is the smallest \textit{k} for which \textit{G} has an edge graceful irregular \textit{s-}labeling. In this paper we determine the exact value of an edge graceful irregularity strength of graphs, namely gear, helm, closed helm and flower graph.