Ranks, Subdegrees and Suborbital Graphs of Symmetric Group Sn Acting on Ordered Pairs
DOI:
https://doi.org/10.53555/nnas.v3i2.664Keywords:
Ranks, Subdegrees, uborbitals, Suborbital graphs, Ordered pairsAbstract
In this research paper, we study the ranks and subdegrees of the symmetric group Sn (n = 3, 4, 5) acting on ordered pairs from the set X = {1, 2 , … , n}. When Sn (n ? 4) acts on ordered pairs from X, the rank is 7. Therefore the main study will be on the ranks and subdegrees of the suborbitals. The suborbital graphs corresponding to the suborbitals of these actions are also constructed. The graph theoretic properties of these suborbital graphs are also discussed. When Sn (n ? 4) acts on ordered pairs, the suborbital graphs, ?1,?2, ?5, and ?6 corresponding to the non-trivial suborbits, ?1 , ?2 , ?5and ?6 are disconnected, regular and undirected. The suborbital graphs ?3and ?4 are disconnected, and directed.
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