Path Embeddings with Prescribed Edge in the Balanced Hypercube Network
نویسندگان
چکیده
Abstract: The balanced hypercube network, which is a novel interconnection network for parallel computation and data processing, is a newly-invented variant of the hypercube. The particular feature of the balanced hypercube is that each processor has its own backup processor and they are connected to the same neighbors. A Hamiltonian bipartite graph with bipartition V0 ∪V1 is Hamiltonian laceable if there exists a path between any two vertices x ∈ V0 and y ∈ V1. It is known that each edge is on a Hamiltonian cycle of the balanced hypercube. In this paper, we prove that, for an arbitrary edge e in the balanced hypercube, there exists a Hamiltonian path between any two vertices x and y in different partite sets passing through e with e 6= xy. This result improves some known results.
منابع مشابه
Optimal Dynamic Edge-Disjoint Embeddings of Complete Binary Trees into Hypercubes
The double-rooted complete binary tree is a complete binary tree where the path (of length ) between the children of the root is replaced by a path of length . It is folklore that the double-rooted complete binary tree is a spanning tree of the hypercube of the same size. Unfortunately, the usual construction of an embedding of a double-rooted complete binary tree into the hypercube does not pr...
متن کاملHypercube Bivariate-Based Key Management for Wireless Sensor Networks
Wireless sensor networks are composed of very small devices, called sensor nodes,for numerous applications in the environment. In adversarial environments, the securitybecomes a crucial issue in wireless sensor networks (WSNs). There are various securityservices in WSNs such as key management, authentication, and pairwise keyestablishment. Due to some limitations on sensor nodes, the previous k...
متن کاملEfficient Embeddings into Hypercube-like Topologies
Embeddings of various graph classes into hypercubes have been widely studied. Almost all these classes are regularly structured graphs such as meshes, complete trees or pyramids. In this paper, we present a general method for one-to-one embeddings of irregularly structured graphs into their optimal hypercubes, based on extended edge bisectors of graphs. An extended edge bisector is an edge bise...
متن کاملEmbedding of Hypercubes into Grids
We consider one-to-one embeddings of the n-dimensional hypercube into grids with 2n vertices and present lower and upper bounds and asymptotic estimates for minimal dilation, edge-congestion, and their mean values. We also introduce and study two new cost-measures for such embeddings, namely the sum over i = 1, ..., n of dilations and the sum of edge congestions caused by the hypercube edges of...
متن کاملA systematic approach for finding Hamiltonian cycles with a prescribed edge in crossed cubes
The crossed cube is one of the most notable variations of hypercube, but some properties of the former are superior to those of the latter. For example, the diameter of the crossed cube is almost the half of that of the hypercube. In this paper, we focus on the problem embedding a Hamiltonian cycle through an arbitrary given edge in the crossed cube. We give necessary and sufficient condition f...
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:
- Symmetry
دوره 9 شماره
صفحات -
تاریخ انتشار 2017