Incidence matrices of projective planes and of some regular bipartite graphs of girth 6 with few vertices
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Data publicació2008-11
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Abstract
Let q be a prime power and r=0,1...,q−3. Using the Latin squares obtained by
multiplying each entry of the addition table of the Galois field of order q by an element
distinct from zero, we obtain the incidence matrices of projective planes and the incidence matrices of (q−r)-regular bipartite graphs of girth 6 and $q^2$−rq−1 vertices in each partite set. Moreover, in this work two Latin squares of order q−1 with entries belonging to {0,1,..., q}, not necessarily the same, are defined to be quasi row-disjoint if and only if the cartesian product of any two rows contains at most one pair (χ,χ) with χ≠0. Using
these quasi row-disjoint Latin squares we find (q−1)-regular bipartite graphs of girth 6 with $q^2$−q−2 vertices in each partite set. Some of these graphs have the smallest number of vertices known so far among the regular graphs with girth 6.
CitacióBalbuena, C. Incidence matrices of projective planes and of some regular bipartite graphs of girth 6 with few vertices. "SIAM journal on discrete mathematics", Novembre 2008, vol. 22, núm. 4, p. 1351-1363.
ISSN0895-4801
Versió de l'editorhttp://www-ma3.upc.es/users/balbuena/PAPERS/Girth6.pdf
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