منابع مشابه
Note: Pancyclicity of the Prism
We show that for every 3-connected cubic graph G, the prism G×K2 has cycles of every even length. Furthermore, if G has a triangle, then G × K2 is pancyclic.
متن کاملNode-pancyclicity and edge-pancyclicity of hypercube variants
Twisted cubes, crossed cubes, Möbius cubes, and locally twisted cubes are some of the widely studied hypercube variants. The 4-pancyclicity of twisted cubes, crossed cubes, Möbius cubes, locally twisted cubes and the 4-edgepancyclicity of crossed cubes are proven in [2, 1, 5, 10, 6] respectively. It should be noted that 4-edge-pancyclicity implies 4-node-pancyclicity which further implies 4-pan...
متن کاملOn the stability for pancyclicity
A property P defined on all graphs of order n is said to be k-stable if for any graph of order n that does not satisfy P , the fact that uv is not an edge of G and that G+uv satisfies P implies dG(u)+dG(v) < k. Every property is (2n−3)-stable and every k-stable property is (k+1)stable. We denote by s(P ) the smallest integer k such that P is k-stable and call it the stability of P . This number...
متن کاملGeodesic pancyclicity and balanced pancyclicity of the generalized base-b hypercube
Recently, Chan et al. have proposed a new cycle embedding property called balanced pancyclicity [Discrete Applied Mathematics 155(15) (2007) 1971-1978]. For a graph G(V, E) and any two nodes x and y of V, a cycle R contains x and y can be divided into two paths, Pt1 and Pt2, joining x and y such that len(Pt1)len(Pt2), where len() denote the length of the path . A balanced cycle of an even (r...
متن کاملForbidden Subgraphs and Pancyclicity
We prove that every 2{connected K 1;3-free and Z 3 ?free graph is hamiltonian except for two graphs. Furthermore, we give a complete characterization of all 2?connected, K 1;3-free graphs, which are not pancyclic, and which are Z 3-free, B-free, W-free, or HP 7 ?free.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2001
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00397-6