Abstract
In this paper, we investigate a measure of similarity of graphs similar to the Ramsey number. We present values and bounds for g(n, l), the biggest number k guaranteeing that there exist l graphs on n vertices, each two having edit distance at least k. By edit distance of two graphs G, F we mean the number of edges needed to be added to or deleted from graph G to obtain graph F. This new extremal number g(n, l) is closely linked to the edit distance of graphs. Using probabilistic methods we show that g(n, l) is close to \(\frac{1} {2}\left( {\begin{array}{*{20}c} n \\ 2 \\ \end{array} } \right)\) for small values of l > 2. We also present some exact values for small n and lower bounds for very large l close to the number of non-isomorphic graphs of n vertices.
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This research was partially supported by the Polish National Science Centre grant number 2011/02/A/ST6/00201.
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Dzido, T., Krzywdziński, K. Edit distance measure for graphs. Czech Math J 65, 829–836 (2015). https://doi.org/10.1007/s10587-015-0211-4
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DOI: https://doi.org/10.1007/s10587-015-0211-4