Cycle embedding of augmented cubes
نویسندگان
چکیده
A graph G 1⁄4 ðV ;EÞ is vertex-pancyclic if for every vertex u and any integer l ranging from a positive constant L to jV j, G contains a cycle C of length l such that u is in C. In this paper, we show that an n-dimensional augmented cube, where n P 2, is vertex-pancyclic with L 1⁄4 3. 2007 Elsevier Inc. All rights reserved.
منابع مشابه
Geodesic-pancyclicity and fault-tolerant panconnectivity of augmented cubes
Choudum and Sunitha [Networks 40 (2002) 71–84] proposed the class of augmented cubes as a variation of hypercubes and showed that augmented cubes possess several embedding properties that the hypercubes and other variations do not possess. Recently, Hsu et al. [Information Processing Letters 101 (2007) 227–232] showed that the ndimensional augmented cube AQn, n 2, is weakly geodesic-pancyclic, ...
متن کاملFault-tolerant pancyclicity of augmented cubes
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...
متن کاملEmbedding Variants of Hypercubes with Dilation
Graph embedding has been known as a powerful tool for implementation of parallel algorithms and simulation of interconnection networks. In this paper, we introduce a technique to obtain a lower bound for the dilation of an embedding. Moreover, we give algorithms for embedding variants of hypercubes with dilation 2 proving that the lower bound obtained is sharp. Further, we compute the exact wir...
متن کاملFault-Tolerant Cycle Embedding in Restricted Hypercube-like Networks with More Faulty Nodes
The hypercube-like networks are a class of important generalization of the popular hypercube interconnection networks for parallel computing. This paper is concerned with the fault-tolerant cycle embedding ability of a subclass of hypercube-like networks, called restricted hypercube-like networks (RHLNs, for short), which include most of the well-known hypercube variants, such as the twisted cu...
متن کاملA Linear Algorithm for Embedding of Cycles in Crossed Cubes with Edge-Pncyclic
A cycle structure is a fundamental network for multiprocessor systems and suitable for developing simple algorithms with low communication cost. Many efficient algorithms were designed with respect to cycles for solving a variety of algebraic problems, graph problems, and some parallel applications, such as those in image and signal processing [2, 16]. To carry out a cycle-structure algorithm o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 191 شماره
صفحات -
تاریخ انتشار 2007