Name
Abstract | ||
|---|---|---|
Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph @C with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of @C, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edge-distance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.jcta.2011.04.011 | Electronic Notes in Discrete Mathematics |
Keywords | DocType | Volume |
spectral excess theorem,quasi-spectral characterization,distance-regular graph,generalized odd graph,intersection number,nonbipartite graph,incidence matrix,k-incidence matrix,degree k,orthogonal polynomials,edge-distance-regular graph,adjacency matrix,completely regular code,orthogonal polynomial,distance regular graph | Journal | 118 |
Issue | ISSN | Citations |
7 | Journal of Combinatorial Theory, Series A | 1 |
PageRank | References | Authors |
0.36 | 11 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. Cámara | 1 | 1 | 0.36 |
| Cristina Dalfó | 2 | 46 | 9.47 |
| josep m fabrega | 3 | 1 | 0.70 |
| M. A. Fiol | 4 | 816 | 87.28 |
| E. Garriga | 5 | 164 | 19.92 |