Isomorphism checking of I-graphs

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Title:	Isomorphism checking of I-graphs
Authors:	ID Horvat, Boris (Author) ID Pisanski, Tomaž (Author) ID Žitnik, Arjana (Author)
Files:	http://dx.doi.org/10.1007/s00373-011-1086-2
Language:	English
Work type:	Not categorized
Typology:	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
PID:	20.500.12556/RUP-444
ISSN:	0911-0119
UDC:	519.17
COBISS.SI-ID:	16069977
Publication date in RUP:	15.10.2013
Views:	5530
Downloads:	139
Metadata:
:	HORVAT, Boris, PISANSKI, Tomaž and ŽITNIK, Arjana, 2012, Isomorphism checking of I-graphs. [online]. 2012. Vol. 28, no. 6, p. 823–830. [Accessed 19 March 2025]. Retrieved from: http://dx.doi.org/10.1007/s00373-011-1086-2 Copy citation

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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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