Open AccessRanks, Subdegrees and Suborbital Graphs of Symmetric Group Sn Acting on Ordered Pairs
Author(s) -
Loyford Njagi
Publication year - 2016
Publication title -
journal of advance research in applied science
Language(s) - English
Resource type - Journals
ISSN - 2208-2352
DOI - 10.53555/nnas.v3i2.664
Subject(s) - combinatorics , mathematics , graph , rank (graph theory) , undirected graph , group (periodic table) , physics , quantum mechanics
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.