Edge-Transitivity of Cayley Graphs Generated by Transpositions

Edge-Transitivity of Cayley Graphs Generated by Transpositions

Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T(S) whenever (i, j) ∈ S. In the present note, it is proved that two transposition graphs ar...

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Bibliographic Details
Main Author: Ganesan Ashwin
Format: Article
Language:English
Published: Sciendo 2016-11-01
Series:Discussiones Mathematicae Graph Theory
Subjects:
cayley graphs
transpositions
automorphisms of graphs
edge-transitive graphs
line graphs
whitney’s isomorphism theorem
Online Access:https://doi.org/10.7151/dmgt.1903
Description
Summary:Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T(S) whenever (i, j) ∈ S. In the present note, it is proved that two transposition graphs are isomorphic if and only if the corresponding two Cayley graphs are isomorphic. It is also proved that the transposition graph T(S) is edge-transitive if and only if the Cayley graph Cay(Sn, S) is edge-transitive.
ISSN:2083-5892

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