Two combinatorial methods for constructing a family of symmetric trivalent graphs are presented in this paper. Each family of graphs contains a member for every odd prime number p. It is proved that in one of the families the girth is unbounded as a function of p; the other family contains the smallest known trivalent graphs of girth 18 and 19.
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IFT UNESP, ICTP South Amer Inst Fundamental Res, BR-01440070 Sao Paulo, SP, BrazilIFT UNESP, ICTP South Amer Inst Fundamental Res, BR-01440070 Sao Paulo, SP, Brazil
Bercini, Carlos
Goncalves, Vasco
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IFT UNESP, ICTP South Amer Inst Fundamental Res, BR-01440070 Sao Paulo, SP, Brazil
Univ Porto, Fac Ciencias, Ctr Fis Porto, P-4169007 Porto, Portugal
Univ Porto, Fac Ciencias, Dept Fis & Astron, P-4169007 Porto, PortugalIFT UNESP, ICTP South Amer Inst Fundamental Res, BR-01440070 Sao Paulo, SP, Brazil
Goncalves, Vasco
Homrich, Alexandre
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Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, CanadaIFT UNESP, ICTP South Amer Inst Fundamental Res, BR-01440070 Sao Paulo, SP, Brazil
Homrich, Alexandre
Vieira, Pedro
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IFT UNESP, ICTP South Amer Inst Fundamental Res, BR-01440070 Sao Paulo, SP, Brazil
Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, CanadaIFT UNESP, ICTP South Amer Inst Fundamental Res, BR-01440070 Sao Paulo, SP, Brazil