Abstract
A cyclic base ordering of a connected graph G is a cyclic ordering of E(G) such that every cyclically consecutive \(|V(G)|-1\) edges induce 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 \(d(H)\le d(G)\) for every connected subgraph H of G. It was conjectured by Kajitani, Ueno and Miyano that G has a cyclic base ordering if and only if G is uniformly dense. In this paper, we study cyclic base ordering of generalized Petersen graphs to support this conjecture.
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Gu, X., Zhang, W. (2022). Cyclically Orderable Generalized Petersen Graphs. In: Ni, Q., Wu, W. (eds) Algorithmic Aspects in Information and Management. AAIM 2022. Lecture Notes in Computer Science, vol 13513. Springer, Cham. https://doi.org/10.1007/978-3-031-16081-3_26
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DOI: https://doi.org/10.1007/978-3-031-16081-3_26
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