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- W2089129796 abstract "A graph G is called pancyclic if it contains a cycle of length I for each integer I from 3 to |V(G)| inclusive, where |V(G)| denotes the cardinality of the vertex set of graph G. It has been shown by Ma et al. (2007) that the augmented cube, proposed by Choudum and Sunitha (2002), is pancyclic. In this paper, we propose a more refined property, namely double-pancyclicity. Let G be a pancyclic graph with N vertices, and (u1, v1), (u2, v2) be any two vertex-disjoint edges in G. Moreover, let l1 and l2 be any two integers of {3, 4,. .., N - 3} such that l1 + l2 N. Then G is said to be double-pancyclic if it has two vertex-disjoint cycles, C1 and C2, such that |V(Ci)| = li and (ui, vi) ∈ E(Ci) for i = 1,2. Moreover, we show that the class of augmented cubes can be almost double-pancyclic." @default.
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- W2089129796 date "2010-01-01" @default.
- W2089129796 modified "2023-09-24" @default.
- W2089129796 title "On the double-pancyclicity of augmented cubes" @default.
- W2089129796 doi "https://doi.org/10.1049/cp.2010.0576" @default.
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