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Title:Isomorphism checking of I-graphs
Authors:Horvat, Boris (Author)
Pisanski, Tomaž (Author)
Žitnik, Arjana (Author)
Files:URL http://dx.doi.org/10.1007/s00373-011-1086-2
 
Language:English
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract: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.
Keywords:mathematics, graph theory, isomorphism, I-graph, generalized Petersen graph
Year of publishing:2012
Number of pages:str. 823-830
Numbering:Vol. 28, no. 6
ISSN:0911-0119
UDC:519.17
COBISS_ID:16069977 Link is opened in a new window
Views:1601
Downloads:76
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Secondary language

Language:Slovenian
Abstract: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.
Keywords:matematika, teorija grafov, izomorfizem, I-graf, posplošeni Petersenov graf

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