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QUASI m-CAYLEY STRONGLY REGULAR GRAPHS
Kutnar, Klavdija,Malnic, Aleksander,Martinez, Luis,Marusic, Dragan Korean Mathematical Society 2013 대한수학회지 Vol.50 No.6
We introduce a new class of graphs, called quasi $m$-Cayley graphs, having good symmetry properties, in the sense that they admit a group of automorphisms G that fixes a vertex of the graph and acts semiregularly on the other vertices. We determine when these graphs are strongly regular, and this leads us to define a new algebro-combinatorial structure, called quasi-partial difference family, or QPDF for short. We give several infinite families and sporadic examples of QPDFs. We also study several properties of QPDFs and determine, under several conditions, the form of the parameters of QPDFs when the group G is cyclic.
Quasi m-Cayley strongly regular graphs
Klavdija Kutnar,Luis Martinez,Aleksander Malnic,Dragan Marusic 대한수학회 2013 대한수학회지 Vol.50 No.6
We introduce a new class of graphs, called quasi m-Cayleygraphs, having good symmetry properties, in the sense that they admita group of automorphisms G that fixes a vertex of the graph and actssemiregularly on the other vertices. We determine when these graphs arestrongly regular, and this leads us to define a new algebro-combinatorialstructure, called quasi-partial difference family, or QPDF for short. Wegive several infinite families and sporadic examples of QPDFs. We alsostudy several properties of QPDFs and determine, under several condi-tions, the form of the parameters of QPDFs when the group G is cyclic.