| Title: | A theorem on Wiener-type invariants for isometric subgraphs of hypercubes |
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| Authors: | ID Klavžar, Sandi (Author)
ID Gutman, Ivan (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.aml.2005.12.004
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | PEF - Faculty of Education
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| Abstract: | Let ▫$d(G,k)$▫ be the number of pairs of vertices of a graph ▫$G$▫ that are at distance ▫$k$▫, ▫$lambda$▫ a real (or complex) number, and ▫$W_lambda(G) = sum_{k ge 1}d(G,k)k^lambda$▫. It is proved that for a partial cube ▫$G$▫, ▫$W_{lambda + 1}(G) = |mathcal{F}| W_lambda(G) - sum_{mathnormal{F} in mathcal{F}} W_lambda(G setminus F)$▫ where ▫$mathcal{F}$▫ is the partition of ▫$E(G)$▫ induced by the Djokovic-Winkler relation ▫$Theta$▫. This result extends a previously known result for trees and implies several relations for distance-based topological indices. |
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| Keywords: | mathematics, graph theory, graph distance, hypercube, partial cube, Wiener number, hyper-Wiener indeks |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publisher: | Elsevier |
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| Year of publishing: | 2006 |
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| Number of pages: | str. 1129-1133 |
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| Numbering: | Letn. 19, št.. 10 |
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| PID: | 20.500.12556/DKUM-51558  |
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| UDC: | 519.17 |
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| ISSN on article: | 0893-9659 |
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| COBISS.SI-ID: | 14040665 |
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| NUK URN: | URN:SI:UM:DK:VCCIRZ28 |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 1559 |
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| Downloads: | 133 |
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| Metadata: |    |
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| Categories: | Misc.
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