Edge-Transitivity of Cayley Graphs Generated by Transpositions

Ashwin Ganesan

Discussiones Mathematicae Graph Theory (2016)

  • Volume: 36, Issue: 4, page 1035-1042
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Ashwin Ganesan. "Edge-Transitivity of Cayley Graphs Generated by Transpositions." Discussiones Mathematicae Graph Theory 36.4 (2016): 1035-1042. <http://eudml.org/doc/287145>.

@article{AshwinGanesan2016,
abstract = {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.},
author = {Ashwin Ganesan},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {Cayley graphs; transpositions; automorphisms of graphs; edge-transitive graphs; line graphs; Whitney’s isomorphism theorem; Whitney's isomorphism theorem},
language = {eng},
number = {4},
pages = {1035-1042},
title = {Edge-Transitivity of Cayley Graphs Generated by Transpositions},
url = {http://eudml.org/doc/287145},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Ashwin Ganesan
TI - Edge-Transitivity of Cayley Graphs Generated by Transpositions
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 4
SP - 1035
EP - 1042
AB - 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.
LA - eng
KW - Cayley graphs; transpositions; automorphisms of graphs; edge-transitive graphs; line graphs; Whitney’s isomorphism theorem; Whitney's isomorphism theorem
UR - http://eudml.org/doc/287145
ER -

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