An infinite series of regular edge‐ but not vertex‐transitive graphs | Zendy

Lazebnik Felix | Zendy; Viglione Raymond | Zendy

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An infinite series of regular edge‐ but not vertex‐transitive graphs

Author(s) -

Lazebnik Felix,

Viglione Raymond

Publication year - 2002

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.10064

Subject(s) - combinatorics , mathematics , symmetric graph , vertex transitive graph , discrete mathematics , regular graph , vertex (graph theory) , prime power , strongly regular graph , transitive relation , petersen graph , circulant graph , graph , voltage graph , line graph , graph power , prime (order theory)

Let n be an integer and q be a prime power. Then for any 3 ≤ n ≤ q −1, or n =2 and q odd, we construct a connected q ‐regular edge‐but not vertex‐transitive graph of order 2 q n +1 . This graph is defined via a system of equations over the finite field of q elements. For n =2 and q =3, our graph is isomorphic to the Gray graph. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 249–258, 2002

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