On the edge-balanced index sets of complete even bipartite graphs
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Authors
Christopher Raridan
Ha Dao
Hung Hua
Michael Ngo
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Journal Article, Academic Journal
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Abstract
In 2009, Kong, Wang, and Lee introduced the problem of finding the edge-balanced index sets ($EBI$) of complete bipartite graphs $K_{m,n}$ by examining the cases where $m \geq n$ and $n=1$, $2$, $3$, $4$, and $5$, as well as the case where $m=n \geq 6$. Since then, the problem of finding $EBI(K_{m,n})$ has been solved in the case where $m \geq n \geq 1$ are both odd and in the case where $m$ is odd, $n$ is even, and $m > n$. In this paper, we find the edge-balanced index sets for complete even bipartite graphs. That is, we solve the $EBI(K_{m,n})$ problem in the case where $m \geq n \geq 2$ are both even.