论文信息 - Distance-Regular Graphs with Diameter Three

Distance-Regular Graphs with Diameter Three

A distance-regular graph of diameter three is a natural generalization of a strongly regular graph, its structure being determined by five parameters. In this paper the feasibility conditions for such graphs are surveyed, and a classification scheme is set up. Constructions and examples for the various cases are given.

N. L. Biggs

[1] N. Biggs. Automorphic graphs and the Krein condition , 1976 .

[2] Derek H. Smith. Primitive and imprimitive graphs , 1971 .

[3] Ernest Shult. The graph extension theorem , 1972 .

[4] D. G. Higman. Invariant Relations, Coherent Configurations and Generalized Polygons , 1975 .

[5] D. E. Taylor. Regular 2‐Graphs , 1977 .

[6] Joseph A. Thas. Two infinite classes of perfect codes in metrically regular graphs , 1977, J. Comb. Theory, Ser. B.

[7] Jonathan I. Hall. Locally petersen graphs , 1980, J. Graph Theory.

[8] Alan J. Hoffman,et al. On Moore Graphs with Diameters 2 and 3 , 1960, IBM J. Res. Dev..

[9] A. Gewirtz,et al. Graphs with Maximal Even Girth , 1969, Canadian Journal of Mathematics.

[10] K. S. Vijayan. On a class of distance transitive graphs , 1978, J. Comb. Theory, Ser. B.

[11] The construction of some automorphic graphs , 1981 .

[12] A. Gardiner. Antipodal covering graphs , 1974 .

[13] Felix Klein,et al. Ueber die Transformation siebenter Ordnung der elliptischen Functionen , 1878 .