dc.contributor.author Ananchuen, Watcharaphong dc.contributor.author Caccetta, Louis dc.date.accessioned 2017-01-30T12:03:05Z dc.date.available 2017-01-30T12:03:05Z dc.date.created 2014-10-28T02:31:41Z dc.date.issued 2006 dc.identifier.citation Ananchuen, W. and Caccetta, L. 2006. Cubic and quadruple Paley graphs with the n-e.c. property. Discrete Mathematics. 306 (22): pp. 2954-2961. dc.identifier.uri http://hdl.handle.net/20.500.11937/17637 dc.description.abstract A graph G is n-existentially closed or n-e.c. if for any two disjoint subsets A and B of vertices of G with |A ∪ B| = n, there is a vertex u /∈A ∪ B that is adjacent to every vertex of A but not adjacent to any vertex of B. It is well-known that almost all graphs are n-e.c. However, few classes of n-e.c. graphs have been constructed. A good construction is the Paley graphs which are defined as follows. Let q ≡ 1(mod 4) be a prime power. The vertices of Paley graphs are the elements of the finite field Fq. Two vertices a and b are adjacent if and only if their difference is a quadratic residue. Previous results established that Paley graphs are n-e.c. for sufficiently large q. By using higher order residues on finite fields we can generate other classes of graphs which we called cubic and quadruple Paley graphs. We show that cubic Paley graphs are n-e.c. whenever q_n224n−2 and quadruple Paley graphs are n-e.c. whenever q_9n262n−2.We also investigate a similar adjacency property for quadruple Paley digraphs. dc.publisher Elsevier Science BV dc.relation.uri http://www.elsevier.com/wps/find/journaldescription.cws_home/505610/description#description dc.title Cubic and quadruple Paley graphs with the n-e.c. property dc.type Journal Article dcterms.source.volume 306 dcterms.source.number 22 dcterms.source.startPage 2954 dcterms.source.endPage 2961 dcterms.source.issn 0012365X dcterms.source.title Discrete Mathematics curtin.accessStatus Fulltext not available
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