The orbit graph for some finite solvable groups
Let G be a finite non-abelian solvable group and let Ω be the set of all subsets of commuting elements of size two in G. In this paper, we define a graph which is called an orbit graph whose vertices are non-central elements in Ω, where two vertices ν1 and ν2 are adjacent in the graph whenever ν1g =...
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| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Published: |
2014
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/62991/ http://dx.doi.org/10.1063/1.4882585 |
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| Summary: | Let G be a finite non-abelian solvable group and let Ω be the set of all subsets of commuting elements of size two in G. In this paper, we define a graph which is called an orbit graph whose vertices are non-central elements in Ω, where two vertices ν1 and ν2 are adjacent in the graph whenever ν1g = ν2, where ν1, ν2 ∈Ω, g ∈G. In this work, we find the orbit graph for some finite solvable groups where a group acts regularly and by conjugation on a set. Besides, some graph properties are found. |
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