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- W2884935356 abstract "Every Steiner triple system is a uniform hypergraph. The coloring of hypergraph and its special case Steiner triple systems, {STS}$(v)$, is studied extensively. But the defining set of the coloring of hypergraph even its special case {STS}$(v)$, is not explored yet. We study minimum defining set and the largest minimal defining set for $3$-coloring of {STS}$(v)$. We determined minimum defining set and the largest minimal defining set, for all non-isomorphic {STS}$(v)$, $vle 15$. Also we have found the {sf defining number} for all Steiner triple systems of order $v$, and some lower bounds for the size of the largest minimal defining set for all Steiner triple systems of order $v$, for each admissible $v$." @default.
- W2884935356 created "2018-08-03" @default.
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- W2884935356 date "2018-07-22" @default.
- W2884935356 modified "2023-10-14" @default.
- W2884935356 title "Determination of the size of defining set for Steiner triple systems" @default.
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- W2884935356 doi "https://doi.org/10.48550/arxiv.1807.08277" @default.
- W2884935356 hasPublicationYear "2018" @default.
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