The Transitive Graphs with at Most 26 Vertices

We complete the construction of all the simple graphs with at most 26 ver- tices and transitive automorphism group. The transitive graphs with up to 19 vertices were earlier constructed by McKay, and the transitive graphs with 24 vertices by Praeger and Royle. Although most of the construction was done by computer, a substantial preparation was necessary. Some of this theory may be on independent interest.

[1]  M. Aschbacher.  A homomorphism theorem for finite graphs , 1976 .

[2]  Dragan Marui.  On vertex symmetric digraphs , 1981 .

[3]  B. Elspas,et al.  Graphs with circulant adjacency matrices , 1970 .

[4]  Jonathan I. Hall.  Graphs with constant link and small degree or order , 1985, J. Graph Theory.

[5]  Bolyai János Matematikai Társulat,et al.  Combinatorial theory and its applications , 1970 .

[6]  J. Seidel.  Graphs and two-graphs , 1974 .

[7]  Wilfried Imrich,et al.  Transitive planar graphs , 1979 .

[8]  A. K. Dewdney,et al.  Generating the nine-point graphs , 1974 .

[9]  Cheryl E. Praeger,et al.  Constructing the Vertex-Transitive Graphs of Order 24 , 1989, J. Symb. Comput..

[10]  Peter Lorimer,et al.  Vertex-transitive graphs: Symmetric graphs of prime valency , 1984, J. Graph Theory.

[11]  B. Weisfeiler.  On construction and identification of graphs , 1976 .

[12]  B. McKay.  Transitive graphs with fewer than twenty vertices , 1979 .

[13]  M. Watkins.  Connectivity of transitive graphs , 1970 .

[14]  Gordon F. Royle.  Constructive enumeration of graphs , 1988, Bulletin of the Australian Mathematical Society.

[15]  B. McKay,et al.  Feasibility conditions for the existence of walk-regular graphs , 1980 .

[16]  C. Praeger.  ON TRANSITIVE PERMUTATION GROUPS WITH A SUBGROUP SATISFYING A CERTAIN CONJUGACY CONDITION , 1984 .

[17]  Brian Alspach,et al.  VERTEX‐TRANSITIVE GRAPHS OF ORDER 2p , 1979 .

[18]  Peter Lorimer,et al.  Trivalent Symmetric Graphs of Order at most 120 , 1984, Eur. J. Comb..