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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doaj-13bd33e305d8469a94640fd6cf1ec8962021-09-05T17:20:22ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922016-11-013641035104210.7151/dmgt.1903dmgt.1903Edge-Transitivity of Cayley Graphs Generated by TranspositionsGanesan Ashwin053 Deonar House, Deonar Village Road, Deonar Mumbai 400088, Maharashtra, IndiaLet 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.https://doi.org/10.7151/dmgt.1903cayley graphstranspositionsautomorphisms of graphsedge-transitive graphsline graphswhitney’s isomorphism theorem |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ganesan Ashwin |
spellingShingle |
Ganesan Ashwin Edge-Transitivity of Cayley Graphs Generated by Transpositions Discussiones Mathematicae Graph Theory cayley graphs transpositions automorphisms of graphs edge-transitive graphs line graphs whitney’s isomorphism theorem |
author_facet |
Ganesan Ashwin |
author_sort |
Ganesan Ashwin |
title |
Edge-Transitivity of Cayley Graphs Generated by Transpositions |
title_short |
Edge-Transitivity of Cayley Graphs Generated by Transpositions |
title_full |
Edge-Transitivity of Cayley Graphs Generated by Transpositions |
title_fullStr |
Edge-Transitivity of Cayley Graphs Generated by Transpositions |
title_full_unstemmed |
Edge-Transitivity of Cayley Graphs Generated by Transpositions |
title_sort |
edge-transitivity of cayley graphs generated by transpositions |
publisher |
Sciendo |
series |
Discussiones Mathematicae Graph Theory |
issn |
2083-5892 |
publishDate |
2016-11-01 |
description |
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. |
topic |
cayley graphs transpositions automorphisms of graphs edge-transitive graphs line graphs whitney’s isomorphism theorem |
url |
https://doi.org/10.7151/dmgt.1903 |
work_keys_str_mv |
AT ganesanashwin edgetransitivityofcayleygraphsgeneratedbytranspositions |
_version_ |
1717786438030852096 |