Premium
The complete bipartite graphs with a unique edge‐transitive embedding
Author(s) -
Fan Wenwen,
Li Cai Heng
Publication year - 2018
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.22176
Subject(s) - bipartite graph , combinatorics , mathematics , complete bipartite graph , embedding , transitive relation , edge transitive graph , robertson–seymour theorem , discrete mathematics , cograph , 1 planar graph , graph , line graph , voltage graph , computer science , artificial intelligence
Jones, Nedela, and Škoviera (2008) showed that a complete bipartite graph K n , nhas a unique orientably regular embedding if and only if gcd ( n , φ ( n ) ) = 1 . In this article, we extend this result by proving that a complete bipartite graph K m , nhas a unique orientably edge‐transitive embedding if and only if gcd ( m , φ ( n ) ) = 1 = gcd ( n , φ ( m ) ) .
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom