2026-04-17T06:25:21Zhttps://recercat.cat/oai/request

oai:recercat.cat:10459.1/725572024-12-05T22:42:41Zcom_2072_3622col_2072_479130

00925njm 22002777a 4500 dc Cámara Vallejo, Marc author Dalfó, Cristina author Fàbrega Canudas, José author Fiol Mora, Miguel Ángel author Garriga, Ernest author 2021-12-14T12:25:06Z 2021-12-14T12:25:06Z 2011-12 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 Γ 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 Γ, 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. Supported by the Ministry of Science and Innovation of Spain under project MTM2008- 06620-C03-01 and by the Catalan Research Council under project 2009SGR01387 http://hdl.handle.net/10459.1/72557 Distance-regularity Local spectra Predistance polynomials Edge distance-regular graphs