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...

A graph is said to be pancyclic if it contains cycles of every length from its girth to its order inclusive; and a bipartite graph is said to be bipancyclic if it contains cycles of every even length from its girth to its order. The pancyclicity or the bipancyclicity of a given network is an important factor in determining whether the network’s topology can simulate rings of various lengths. An...

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.

with Local Ore-Type Conditions II A.S. Asratian, R H aggkvist and G.V. Sarkisian University of Ume a January, 1994 Abstract. It is well known due Ore that a graph G of order at least 3 is Hamiltonconnected if d(u) + d(v) jV (G)j + 1 for each pair of nonadjacent vertices u and v. We consider here connected graphs G of order at least 3 where d(u) + d(v) jN(u) [N(v) [N(w)j+ 1 for each triple of v...

In this paper, we study the existence of cycles of all lengths in the recursive circulant graphs, and we show a necessary and sufficient condition for the graph being pancyclic and bipancyclic.  2002 Elsevier Science B.V. All rights reserved.

Abstract: A hypertournament or a k-tournament, on n vertices, 2≤k≤n, is a pair T= (V,E), where the vertex setV is a set of size n and the edge setE is the collection of all possible subsets of size k of V, called the edges, each taken in one of its k! possible permutations. A k-tournament is pancyclic if there exists (directed) cycles of all possible lengths; it is vertex-pancyclic if moreover ...

The coupled graph c(G) of a plane graph G is the graph de.ned on the vertex set V (G)∪F(G) so that two vertices in c(G) are joined by an edge if and only if they are adjacent or incident in G. We prove that the coupled graph of a 2-connected plane graph is edge-pancyclic. However, there exists a 2-edge-connected plane graph G such that c(G) is not Hamiltonian. ? 2002 Elsevier Science B.V. All r...