Name
Abstract | ||
|---|---|---|
Let Gamma be a regular graph with n vertices, diameter D, and d + 1 different eigenvalues lambda > lambda(1) > > lambda(d). In a previous paper, the authors showed that if P(lambda) > n - 1, then D less than or equal to d - 1, where P is the polynomial of degree d-1 which takes alternating values +/-1 at lambda(1), ..., lambda(d). The graphs satisfying P(X) = n - 1, called boundary graphs, have shown to deserve some attention because of their rich structure. This paper is devoted to the study of this case and, as a main result, it is shown that those extremal (D = d) boundary graphs where each vertex have maximum eccentricity are, in fact, 2-antipodal distance-regular graphs. The study is carried out by using a new sequence of orthogonal polynomials, whose special properties are shown to be induced by their intrinsic symmetry. (C) 1998 John Wiley & Sons, Inc. |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1002/(SICI)1097-0118(199803)27:3<123::AID-JGT2>3.0.CO;2-Q | Journal of Graph Theory |
Keywords | Field | DocType |
distance regular graph,orthogonal polynomials,eigenvalues | Topology,Odd graph,Discrete mathematics,Random regular graph,Indifference graph,Strongly regular graph,Combinatorics,Chordal graph,1-planar graph,Mathematics,Pancyclic graph,Triangle-free graph | Journal |
Volume | Issue | ISSN |
27 | 3 | 0364-9024 |
Citations | PageRank | References |
12 | 1.65 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. A. Fiol | 1 | 816 | 87.28 |
| E. Garriga | 2 | 164 | 19.92 |
| J. L.A. Yebra | 3 | 291 | 36.48 |