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On Partitional Labelings of Graphs
Mathematics in Computer Science, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rikio Ichishima, Akito Oshima
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A mapping \(f: E\to\{0,1\}^m\) of a graph \(G=(V,E)\) is called a mod 2 coding of \(G\), if the induced mapping \(g:V\to \{0,1\}^m\), defined by \(g(v)= \sum_{u\in V,\{u,v\}\in E}f(\{u,v\})\) assigns a different number to each vertex, where summations are taken modulo 2.
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Summary: Given a graph \(G\) and positive integer \(d\), the pair-labeling number \(r^*(G,d)\) is the minimum \(n\) such that each vertex in \(G\) can be assigned a pair of numbers from \(\{0,1,\dots,n-1\}\) so that any two numbers used at adjacent vertices differ by at least \(d\) modulo \(n\).
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