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
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2012
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str. 823-830
no. 6
Vol. 28
2012
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NiDoloceno
NiDoloceno
NiDoloceno
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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
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