Distance-transitive dihedrants |
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Authors: | ?tefko Miklavi? Primo? Poto?nik |
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Institution: | (1) Department of Mathematics and Computer Science, Faculty of Education, University of Primorska, Cankarjeva 5, 6000 Koper, Slovenia;(2) Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia |
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Abstract: | The main result of this article is a classification of distance-transitive Cayley graphs on dihedral groups. We show that a Cayley graph X on a dihedral group is distance-transitive if and only if X is isomorphic to one of the following graphs: the complete graph K
2n
; a complete multipartite graph K
t×m
with t anticliques of size m, where t
m is even; the complete bipartite graph without 1-factor K
n,n
− nK
2; the cycle C
2n
; the incidence or the non-incidence graph of the projective geometry PG
d-1(d,q), d ≥ 2; the incidence or the non-incidence graph of a symmetric design on 11 vertices. |
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Keywords: | Cayley graph Distance-regular graph Distance-transitive graph Dihedrant Dihedral group Difference set |
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