A side skirt is a planar rooted tree T, T≠P2, where the root of T vertex degree at least two, and all other vertices except leaves are three. reduced Halin graph or skirted plane G=T∪P, skirt, P path connecting in order determined by embedding T. The structure graphs contains both symmetry asymmetry. For n≥2 Pn=v1v2v3⋯vn as length n−1, we call Cartesian product G Pn, n-generalized prism over G....

The Möbius cube MQn proposed by Cull et al. is an alternative to the popular hypercube network. Recently, MQn was shown to be pancyclic, i.e., cycles of any lengths at least four can be embedded into it. Due to the importance of the fault tolerance in the parallel processing area, in this paper, we study an injured MQn with mixed node and link faults. We show that it is (n − 2)-fault-tolerant p...

A graph G on n vertices is Hamiltonian if it contains a cycle of length n and pancyclic if it contains cycles of length ` for all 3 ≤ ` ≤ n. Write α(G) for the independence number of G, i.e. the size of the largest subset of the vertex set that does not contain an edge, and κ(G) for the (vertex) connectivity, i.e. the size of the smallest subset of the vertex set that can be deleted to obtain a...

The OTIS-Network (also referred to as two-level swapped network) is composed of n clones of an n-node original network constituting its clusters. It has received much attention due to its many favorable properties such as high degree of scalability, regularity, modularity, package-ability and high degree of algorithmic efficiency. In this paper, using the construction method, we show that the O...

The locally twisted cube LTQn is a newly introduced interconnection network for parallel computing. As a variant of the hypercube Qn, LTQn has better properties than Qn with the same number of links and processors. Yang, Megson and Evans [Locally twisted cubes are 4pancyclic, Applied Mathematics Letters, 17 (2004), 919-925] showed that LTQn contains a cycle of every length from 4 to 2 . In this...

As an enhancement on the hypercube Qn, the augmented cube AQn, prosed by Choudum and Sunitha [S.A. Choudum, V. Sunitha, Augmented cubes, Networks 40 (2) (2002) 71–84], not only retains some favorable properties of Qn but also possesses some embedding properties that Qn does not. For example, AQn is pancyclic, that is, AQn contains cycles of arbitrary length for n 2. This paper shows that AQn re...

It is known that ff a 2-connected graph G of suiBciently large order n satisfies the property that the union of the neighborhoods of each pair of vertices has cardinallty at least ~-, " then G is hamiltonian. In this paper, we obtain a similar generalization of Dirac's Theorem for K(1, 3)-free graphs. In particular, we show that if G is a 2-connected K(1, 3)-free graph of order n with the cardi...