论文信息 - On distance-regular graphs withki =kj, II

On distance-regular graphs withki =kj, II

LetГ be a distance-regular graph of diameterd andi-th valencyki. We show that ifk2 = kj for 2 +j ≥ d and 2 <j, thenГ is a polygon (k = 2) or an antipodal 2-cover (kd = 1). We also give a short proof of Terwilliger's inequality for bipartite distance-regular graphs and a refinement of Ivanov's argument on diameter bound.

Hiroshi Suzuki | Akira Hiraki | Masayuki Wajima

[1] Tatsuro Ito,et al. On Distance-regular Graphs with Fixed Valency, IV , 1989, Eur. J. Comb..

[2] Hiroshi Suzuki,et al. Bounding the diameter of a distance regular graph by a function ofkd , 1991, Graphs Comb..

[3] A. Neumaier,et al. Distance Regular Graphs , 1989 .

[4] Tatsuro Ito,et al. On distance-regular graphs with fixed valency , 1987, Graphs Comb..

[5] Paul M. Terwilliger. Distance-regular graphs and (s, c, a, k)-graphs , 1983, J. Comb. Theory, Ser. B.

[6] Lu Jia-xi,et al. On Large Sets of Disjoint Steiner Triple Systems, IV , 1983, J. Comb. Theory, Ser. A.

[7] Kazumasa Nomura,et al. A remark on the intersection arrays of distance-regular graphs , 1987, J. Comb. Theory, Ser. B.

[8] Tatsuro Ito,et al. Current research on algebraic combinatorics , 1986, Graphs Comb..

[9] Paul M. Terwilliger. Distance-regular graphs with girth 3 or 4: I , 1985, J. Comb. Theory, Ser. B.

[10] Tatsuro Ito,et al. On distance-regular graphs with fixed valency, III , 1987 .

[11] Hitoshi Suzuki. On Distance-Regular Graphs with ki = kj , 1994, J. Comb. Theory, Ser. B.

[12] E. Bannai,et al. Algebraic Combinatorics I: Association Schemes , 1984 .