Premium
SGDs with doubly transitive automorphism group
Author(s) -
Cameron Peter J.
Publication year - 1999
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/(sici)1097-0118(199911)32:3<229::aid-jgt2>3.0.co;2-c
Subject(s) - transitive relation , mathematics , combinatorics , automorphism , disjoint sets , generalization , graph , group (periodic table) , automorphism group , inner automorphism , discrete mathematics , mathematical analysis , chemistry , organic chemistry
Symmetric graph designs, or SGDs, were defined by Gronau et al. as a common generalization of symmetric BIBDs and orthogonal double covers. This note gives a classification of SGDs admitting a 2‐transitive automorphism group. There are too many for a complete determination, but in some special cases the determination can be completed, such as those that admit a 3‐transitive group, and those with λ = 1. The latter case includes the determination of all near 1‐factorizations of K n (partitions of the edge set into subsets each of which consists of disjoint edges covering all but one point), which admit 2‐transitive groups. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 229–233, 1999