Distance Magic Labeling in Complete 4-partite Graphs |
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Authors: | Daniel Kotlar |
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Institution: | 1.Department of Computer Science,Tel-Hai College,Upper Galilee,Israel |
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Abstract: | Let G be a complete k-partite simple undirected graph with parts of sizes \(p_1\le p_2\cdots \le p_k\). Let \(P_j=\sum _{i=1}^jp_i\) for \(j=1,\ldots ,k\). It is conjectured that G has distance magic labeling if and only if \(\sum _{i=1}^{P_j} (n-i+1)\ge j{{n+1}\atopwithdelims (){2}}/k\) for all \(j=1,\ldots ,k\). The conjecture is proved for \(k=4\), extending earlier results for \(k=2,3\). |
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