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Exceptional trivalent cayley graphs for dihedral groups
Author(s) -
Powers David L.
Publication year - 1982
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190060106
Subject(s) - dihedral group , mathematics , cayley graph , combinatorics , bipartite graph , odd graph , isomorphism (crystallography) , graph isomorphism , discrete mathematics , pancyclic graph , chordal graph , graph , group (periodic table) , 1 planar graph , crystallography , line graph , chemistry , crystal structure , organic chemistry
If n is divisible by at least three distinct primes, the dihedral group D n can be generated by three nonredundant, involuntary elements. We study the Cayley graphs resulting from such a presentation of D n for several families of n and for all admissible n < 120. All these graphs are trivalent, bipartite, Hamiltonian, of girth 6, and are regular representations of their groups. For each n , the isomorphism classes are determined and the graphs are described by a simple code.
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