Abstract
LetG(V,E) be a graph. A mappingf:E→{0,1}m is called a (binary) coding ofG, if the induced mapping\(g:V \to \{ 0,1\} ^m ,g(\upsilon ) = \sum\limits_{e \mathrel\backepsilon v} {f(e)} \), assigns different vectors to the vertices. For the Boolean sum,f is called aB-code, and for the mod 2 sum anM-code. Letm B (G) resp.m M (G) be the smallest lengthm for whichB-codes resp.M-codes are possible. Trivially,m B (G),m M (G) ≥ ⌈log2|V|⌉. Improving results of Z. Tuza we showm B (G)≤⌈log2|V|⌉ + 1,m M (G)≤⌈log2|V|⌉+4.
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Aigner, M., Triesch, E. Codings of graphs with binary edge labels. Graphs and Combinatorics 10, 1–10 (1994). https://doi.org/10.1007/BF01202464
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DOI: https://doi.org/10.1007/BF01202464