20.500.12556/RUP-444 Isomorphism checking of I-graphs We consider the class of ▫$I$▫-graphs, which is a generalization of the class of the generalized Petersen graphs. We show that two ▫$I$▫-graphs ▫$I(n, j, k)$▫ and ▫$I(n, j_1, k_1)$▫ are isomorphic if and only if there exists an integer ▫$a$▫ relatively prime to $n$ such that either ▫$\{j_1, k_1\} = \{aj \mod n, \; ak \mod n \}$▫ or ▫$\{j_1, k_1\} = \{aj \mod n, \; -ak \mod n\}$▫. This result has an application in the enumeration of non-isomorphic ▫$I$▫-graphs and unit-distance representations of generalized Petersen graphs. Obravnavamo razred ▫$I$▫-grafov - posplošitev razreda t.i. posplošenih Petersenovih grafov. Pokažemo da sta ▫$I$▫-grafa ▫$I(n, j, k)$▫ in ▫$I(n, j_1, k_1)$▫ izomorfna natanko takrat, ko obstaja celo število ▫$a$▫ tuje z ▫$n$▫, za katerega velja, da drži bodisi ▫$\{j_1, k_1\} = \{aj \mod n, \; ak \mod n \}$▫ bodisi ▫$\{j_1, k_1\} = \{aj \mod n, \; -ak \mod n\}$▫. Ta rezultat je uporaben pri preštevanju neizomorfnih ▫$I$▫-grafov in predstavitev z enotsko razdaljo posplošenih Petersenovih grafov. mathematics graph theory isomorphism I-graph generalized Petersen graph matematika teorija grafov izomorfizem I-graf posplošeni Petersenov graf true true false Angleški jezik Slovenski jezik Delo ni kategorizirano 2013-10-15 12:04:50 2013-10-15 12:04:50 2024-03-01 11:55:29 0000-00-00 00:00:00 2012 0 0 str. 823-830 no. 6 Vol. 28 2012 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0911-0119 519.17 16069977 http://dx.doi.org/10.1007/s00373-011-1086-2 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=444 Inštitut Andrej Marušič 0 0 0