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Totally symmetric colored graphs
Author(s) -
Grech Mariusz,
Kisielewicz Andrzej
Publication year - 2009
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.20397
Subject(s) - combinatorics , mathematics , colored , permutation group , transitive relation , automorphism , symmetric group , 1 planar graph , discrete mathematics , cograph , graph , permutation (music) , chordal graph , materials science , physics , acoustics , composite material
In this paper we describe almost all edge‐colored complete graphs that are fully symmetric with respect to colors and transitive on every set of edges of the same color. This generalizes the recent description of self‐complementary symmetric graphs by Peisert and gives examples of permutation groups that require more than 5 colors to be represented as the automorphism group of a k ‐colored graph. This also contributes to the recent study of homogeneous factorizations of complete graphs. The result relies on the classification of finite simple groups. © 2009 Wiley Periodicals, Inc. J Graph Theory 62: 329–345, 2009