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- Title
Cyclic base ordering of generalized Petersen graphs.
- Authors
Gu, Xiaofeng; Zhang, William
- Abstract
A cyclic base ordering (CBO) of a connected graph G is a cyclic ordering of E (G) such that every cyclically consecutive | V (G) | − 1 edge induces a spanning tree of G. The density of G is defined to be d (G) = | E (G) | / (| V (G) | − 1) ; and G is uniformly dense if d (H) ≤ d (G) for every connected subgraph H of G. It was conjectured by Kajitani, Ueno and Miyano that G has a CBO if and only if G is uniformly dense. In this paper, we study CBO of generalized Petersen graphs to support this conjecture, and we prove that G (n , 1) and G (n , 2) have CBO.
- Subjects
UNITED States. Congressional Budget Office; PETERSEN graphs; GRAPH connectivity; SPANNING trees
- Publication
Discrete Mathematics, Algorithms & Applications, 2024, Vol 16, Issue 2, p1
- ISSN
1793-8309
- Publication type
Article
- DOI
10.1142/S1793830923500192