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Retarded regular graphs are regular or semiregular |
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| Authors: | José A. De La Peña Ivan Gutman Juan Rada |
| Affiliation: | 1. Instituto de Matemáticas, UNAM. Cd. Universitaria , México 04510, D.F., Mexico jap@matem.unam.mx;3. Faculty of Science, University of Kragujevac , P. O. Box 60, 34000 Kragujevac, Serbia;4. Facultad de Ciencias, Departamento de Matemáticas , Universidad de los Andes , Mérida, Venezuela |
| Abstract: | A graph G is said to be retarded regular if there is a positive integral number s such that the number of walks of length s starting at vertices of G is a constant function. Regular and semiregular graphs are retarded regular with s?=?1 and s!≤ !2, respectively. We prove that any retarded regular connected graph is either regular or semiregular. |
| Keywords: | Retarded regular graphs Adjacency matrix Semiregular graph |