| Title: | On the role of hypercubes in the resonance graphs of benzenoid graphs |
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| Authors: | ID Salem, Khaled (Author)
ID Klavžar, Sandi (Author)
ID Gutman, Ivan (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.disc.2005.11.017
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.03 - Other scientific articles |
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| Organization: | PEF - Faculty of Education
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| Abstract: | The resonance graph ▫$R(B)$▫ of a benzenoid graph ▫$B$▫ has the perfect matchings of ▫$B$▫ as vertices, two perfect matchings being adjacent if their symmetric difference forms the edge set of a hexagon of ▫$B$▫. A family ▫$mathscr{P}$▫ of pair-wise disjoint hexagons of a benzenoid graph ▫$B$▫ is resonant in ▫$B$▫ if ▫$B -- mathscr{P}$▫ contains at least one perfect matching, or if ▫$B -- mathscr{P}$▫ is empty. It is proven that there exists a surjective map ▫$f$▫ from the set of hypercubes of ▫$R(B)$▫ onto the resonant sets of B such that a ▫$k$▫-dimensional hypercube is mapped into a resonant set of cardinality ▫$k$▫. |
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| Keywords: | matematika, teorija grafov, benzenoidni graf, popolno prirejanje, resonančni graf, hiperkocka, mathematics, graph theory, benzenoid graph, perfect matching, resonance graph, hypercube |
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| Year of publishing: | 2006 |
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| Number of pages: | str. 699-704 |
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| Numbering: | Vol. 306, iss. 7 |
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| PID: | 20.500.12556/DKUM-51515  |
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| UDC: | 519.17:541 |
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| ISSN on article: | 0012-365X |
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| COBISS.SI-ID: | 13943641 |
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| NUK URN: | URN:SI:UM:DK:QYUF5WXO |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 1807 |
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| Downloads: | 83 |
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| Metadata: |    |
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| Categories: | Misc.
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