On the Edge-balanced Index Sets of Complete Bipartite Graphs

zbMATH Open1247.05209arXiv1106.1085MaRDI QIDQ3110115

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Publication date: 26 January 2012

Abstract: Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a 0-1 labeling of $E(G)$ so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling $f$ emph{edge-friendly}. The emph{edge-balanced index set} of the graph $G$, $EBI(G)$, is defined as the absolute difference between the number of vertices incident to more edges labeled 1 and the number of vertices incident to more edges labeled 0 over all edge-friendly labelings $f$. In 2009, Lee, Kong, and Wang cite{LeeKongWang} found the $EBI(K_{l,n})$ for $l=1,2,3,4,5$ as well as $l=n$. We continue the investigation of the $EBI$ of complete bipartite graphs of other orders.

Full work available at URL: https://arxiv.org/abs/1106.1085

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