# Edge-Transitivity of Cayley Graphs Generated by Transpositions

Discussiones Mathematicae Graph Theory (2016)

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

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topAshwin 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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