On the primitive idempotents of distance-regular graphs

被引：6
|
作者：
Tomiyama, M [1 ]
机构：
[1] Ishikawa Natl Coll Technol, Dept Gen Educ, Tsubata, Ishikawa 9290392, Japan
来源：
DISCRETE MATHEMATICS | 2001年 / 240卷 / 1-3期
关键词：
distance-regular graph; Q-polynomial; primitive idempotent; eigenvalue; cosine sequence;
D O I：
10.1016/S0012-365X(01)00200-X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let Gamma denote a distance-regular graph with diameter d greater than or equal to 3. Let E, F denote nontrivial primitive idempotents of Gamma such that F corresponds to the second largest or the least eigenvalue. We investigate the situation that there exists a primitive idempotent H of Gamma such that E circle F is a linear combination of F and H. Our main purpose is to obtain the inequalities involving the cosines of E, and to show that equality is closely related to Gamma being Q-polynomial with respect to E. This generalizes a result of Lang on bipartite graphs and a result of Pascasio on tight graphs. (C) 2001 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：281 / 294
页数：14
相关论文
共 50 条
  • [1] Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra
    Terwilliger, P
    Weng, CW
    [J]. EUROPEAN JOURNAL OF COMBINATORICS, 2004, 25 (02) : 287 - 298
  • [2] Bipartite distance-regular graphs: The Q-polynomial property and pseudo primitive idempotents
    Lang, Michael S.
    [J]. DISCRETE MATHEMATICS, 2014, 331 : 27 - 35
  • [3] Pseudo primitive idempotents and almost 2-homogeneous bipartite distance-regular graphs
    Lang, Michael S.
    [J]. EUROPEAN JOURNAL OF COMBINATORICS, 2008, 29 (01) : 35 - 44
  • [4] On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph
    Pascasio, AA
    [J]. EUROPEAN JOURNAL OF COMBINATORICS, 2002, 23 (08) : 1073 - 1078
  • [5] Distance-regular graphs
    van Dam, Edwin R.
    Koolen, Jack H.
    Tanaka, Hajime
    [J]. ELECTRONIC JOURNAL OF COMBINATORICS, 2016, : 1 - 156
  • [6] THE DISTANCE-REGULAR ANTIPODAL COVERS OF CLASSICAL DISTANCE-REGULAR GRAPHS
    VANBON, JTM
    BROUWER, AE
    [J]. COMBINATORICS /, 1988, 52 : 141 - 166
  • [7] The Q -polynomial idempotents of a distance-regular graph
    Jurisic, Aleksandar
    Terwilliger, Paul
    Zitnik, Arjana
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2010, 100 (06) : 683 - 690
  • [8] DISTANCE-REGULAR GRAPHS AND HALVED GRAPHS
    HEMMETER, J
    [J]. EUROPEAN JOURNAL OF COMBINATORICS, 1986, 7 (02) : 119 - 129
  • [9] On automorphisms of distance-regular graphs
    Makhnev A.A.
    [J]. Journal of Mathematical Sciences, 2010, 166 (6) : 733 - 742
  • [10] On almost distance-regular graphs
    Dalfo, C.
    van Dam, E. R.
    Fiol, M. A.
    Garriga, E.
    Gorissen, B. L.
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2011, 118 (03) : 1094 - 1113
12345