Transitivity on Minimum Dominating Sets of Paths and Cycles
Transitivity on graphs is a concept widely investigated. This suggest to analyze the action of automorphisms on other sets. In this paper, we study the action on the family of <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></m...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-12-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/12/2053 |
| Summary: | Transitivity on graphs is a concept widely investigated. This suggest to analyze the action of automorphisms on other sets. In this paper, we study the action on the family of <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-sets (minimum dominating sets), the graph is called <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-transitive if given two <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-sets there exists an automorphism which maps one onto the other. We deal with two families: paths <inline-formula><math display="inline"><semantics><msub><mi mathvariant="normal">P</mi><mi>n</mi></msub></semantics></math></inline-formula> and cycles <inline-formula><math display="inline"><semantics><msub><mi mathvariant="normal">C</mi><mi>n</mi></msub></semantics></math></inline-formula>. Their <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-sets are fully characterized and the action of the automorphism group on the family of <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-sets is fully analyzed. |
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| ISSN: | 2073-8994 |