Isomorphism checking of I-graphs
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;mathematics;graph theory;isomorphism;I-graph;generalized Petersen graph;
Data
| Language: | English |
|---|---|
| Year of publishing: | 2012 |
| Typology: | 1.01 - Original Scientific Article |
| Organization: | UL FMF - Faculty of Mathematics and Physics |
| UDC: | 519.17 |
| COBISS: |
16069977
|
| ISSN: | 0911-0119 |
| Views: | 0 |
| Downloads: | 0 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | Slovenian |
|---|---|
| Secondary title: | Preverjanje izomorfnosti I-grafov |
| Secondary 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. |
| Secondary keywords: | matematika;teorija grafov;izomorfizem;I-graf;posplošeni Petersenov graf; |
| Type (COBISS): | Not categorized |
| Pages: | str. 823-830 |
| Volume: | Vol. 28 |
| Issue: | no. 6 |
| Chronology: | 2012 |
| ID: | 1475866 |
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