Edge distance-regular graphs
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-regu...
| Autores: | ; ; ; ; |
|---|---|
| Tipo de documento: | Artigo |
| Estado: | Accepted version |
| Data de publicação: | 2011 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/72557 |
| Acesso em linha: | https://doi.org/10.1016/j.endm.2011.09.037 http://hdl.handle.net/10459.1/72557 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | Distance-regularity Local spectra Predistance polynomials |
| _version_ | 1878731421231611904 |
|---|---|
| author | Cámara Vallejo, Marc |
| author2 | Dalfó, Cristina Fàbrega Canudas, José Fiol Mora, Miguel Ángel Garriga, Ernest |
| author2_role | author author author author |
| author_browse | Cámara Vallejo, Marc Dalfó, Cristina Fiol Mora, Miguel Ángel Fàbrega Canudas, José Garriga, Ernest |
| author_facet | Cámara Vallejo, Marc Dalfó, Cristina Fàbrega Canudas, José Fiol Mora, Miguel Ángel Garriga, Ernest |
| author_role | author |
| collection | Recercat. Dipósit de la Recerca de Catalunya |
| description | 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_2f3a7535a2f21f68c1c4e9d64ba1df7f |
| institution | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| instname_str | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:recercat.cat:10459.1/72557 |
| publishDate | 2011 |
| publishDateSort | 2011 |
| publisher | Elsevier |
| publisherStr | Elsevier |
| reponame_str | Recercat. Dipósit de la Recerca de Catalunya |
| spelling | Edge distance-regular graphs Cámara Vallejo, Marc Dalfó, Cristina Fàbrega Canudas, José Fiol Mora, Miguel Ángel Garriga, Ernest Distance-regularity Local spectra Predistance polynomials 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 Elsevier https://doi.org/10.1016/j.endm.2011.09.037 http://hdl.handle.net/10459.1/72557 |
| spellingShingle | Edge distance-regular graphs Cámara Vallejo, Marc Distance-regularity Local spectra Predistance polynomials |
| status_str | acceptedVersion |
| title | Edge distance-regular graphs |
| title_full | Edge distance-regular graphs |
| title_fullStr | Edge distance-regular graphs |
| title_full_unstemmed | Edge distance-regular graphs |
| title_short | Edge distance-regular graphs |
| title_sort | Edge distance-regular graphs |
| topic | Distance-regularity Local spectra Predistance polynomials |
| topic_facet | Distance-regularity Local spectra Predistance polynomials |
| url | https://doi.org/10.1016/j.endm.2011.09.037 http://hdl.handle.net/10459.1/72557 |