| Title: | Trees with distinguishing index equal distinguishing number plus one |
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| Authors: | ID Alikhani, Saeid (Author)
ID Klavžar, Sandi (Author)
ID Lehner, Florian (Author)
ID Soltani, Samaneh (Author) |
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| Files: |  Alikhani-2020-TREES_WITH_DISTINGUISHING_INDEX.pdf (144,96 KB)
MD5: 52B8E3DB245D84B546B3F5FD842D8D6A
 https://doi.org/10.7151/dmgt.2162
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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: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | The distinguishing number (index) D(G) (D'(G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism. It is known that for every graph G we have D'(G) \leq D(G) + 1. In this note we characterize finite trees for which this inequality is sharp. We also show that if G is a connected unicyclic graph, then D'(G) = D(G). |
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| Keywords: | automorphism group, distinguishing index, distinguishing number, tree, unicyclic graph |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 15.09.2017 |
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| Article acceptance date: | 13.07.2018 |
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| Publisher: | Technical University Press |
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| Year of publishing: | 2020 |
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| Number of pages: | Str. 875-884 |
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| Numbering: | Letn. 40, št. 3 |
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| PID: | 20.500.12556/DKUM-92004  |
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| UDC: | 519.17 |
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| ISSN on article: | 1234-3099 |
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| COBISS.SI-ID: | 18956889 |
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| DOI: | 10.7151/dmgt.2162 |
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| Publication date in DKUM: | 11.03.2025 |
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| Views: | 103 |
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| Downloads: | 25 |
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| Metadata: |    |
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| Categories: | Misc.
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