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Generalized honeycomb torus

Hsun-Jung Cho, Li-Yen Hsu
2003 Information Processing Letters  
Stojmenovic introduced three different honeycomb tori by adding wraparound edges on honeycomb meshes, namely honeycomb rectangular torus, honeycomb rhombic torus, and honeycomb hexagonal torus.  ...  In this paper, we propose generalized honeycomb tori. The three different honeycomb tori proposed by Stojmenovic are proved to be special cases of our proposed generalized honeycomb tori.  ...  In this paper, we propose a generalized honeycomb torus. We will prove that all the honeycomb tori mentioned above are special cases of the generalized honeycomb torus.  ... 
doi:10.1016/s0020-0190(02)00507-0 fatcat:ngnlxgncurfxnowkg6cd6pter4

Generalized honeycomb torus is Hamiltonian

Xiaofan Yang, David J. Evans, Hongjian Lai, Graham M. Megson
2004 Information Processing Letters  
Generalized honeycomb torus is a candidate for interconnection network architectures, which includes honeycomb torus, honeycomb rectangular torus, and honeycomb parallelogramic torus as special cases.  ...  Lett. 86 (4) (2003) 185-190] speculated that every generalized honeycomb torus is Hamiltonian. In this paper, we have proved this conjecture.  ...  It is known [3] that generalized honeycomb torus includes honeycomb torus, honeycomb rectangular torus, and honeycomb parallelogramic torus as special cases.  ... 
doi:10.1016/j.ipl.2004.05.017 fatcat:hw3jfofmj5ahpjtzydrpge7cre

Ring embedding in faulty generalized honeycomb torus – GHT(m, n, n/2)

Li-Yen Hsu, Feng-I Ling, Shin-Shin Kao, Hsun-Jung Cho
2010 International Journal of Computer Mathematics  
In Section 2, we define some graphing terms that are used in the paper and give a formal definition of the generalized honeycomb torus.  ...  Developing configurations of generalized honeycomb tori.  ...  Consequently, any generalized honeycomb torus is a 3-regular bipartite graph. We are interested in a special type of generalized honeycomb torus, GHT(m, n, n/2).  ... 
doi:10.1080/00207160903315524 fatcat:yht2tc7nzfgbzctdoqsseu4jqq

The diameter of Honeycomb rhombic tori

Xiaofan Yang
2004 Applied Mathematics Letters  
In this paper, the diameter of a honeycomb rhombic torus is determined, which is lower than that of a torus of the same order.  ...  Therefore, the superiority of honeycomb rhombic torus networks is greatly strengthened.  ...  In this paper, we completely determine the diameter of a honeycomb rhombic torus. The result demonstrates that a honeycomb rhombic torus has a diameter smaller than that of a torus of the same order.  ... 
doi:10.1016/s0893-9659(04)90028-6 fatcat:zvb3wz33bneh5ir54kbrr4sg2i

A Survey on Area Planning for Heterogeneous Networks

V.Ceronmani Sharmila, George A
2013 International Journal on Applications of Graph Theory In wireless Ad Hoc Networks And sensor Networks  
This paper deals with the survey of basic networks like Spidergon network and Honeycomb Torus network with respect to network cost.  ...  CONCLUSION In general the Honeycomb Torus network may be having lower network cost, but the networks which are having smaller number of nodes (if number of nodes is ≤ 10) the network cost is less for Spidergon  ...  1.63√ 4.9√ 0.82√ Torus 4 √ 4√ 2√ Hexagonal Torus 6 0.58√ 3.46√ 4.61√ Honeycomb Torus 3 0.81√ 2.45√ 2.04√ Honeycomb Rhombic Mesh 3 2.83√ 8.49√ 0.71√ Honeycomb Square Mesh 3 2√  ... 
doi:10.5121/jgraphoc.2013.5102 fatcat:efov5wvmhbcgtduau7dirxq7q4

A unified formulation of honeycomb and diamond networks

B. Parhami, Ding-Ming Kwai
2001 IEEE Transactions on Parallel and Distributed Systems  
AbstractÐHoneycomb and diamond networks have been proposed as alternatives to mesh and torus architectures for parallel processing.  ...  When wraparound links are included in honeycomb and diamond networks, the resulting structures can be viewed as having been derived via a systematic pruning scheme applied to the links of 2D and 3D tori  ...  Based on the discussion above, generalizing honeycomb and diamond networks to n dimensions is straightforward.  ... 
doi:10.1109/71.899940 fatcat:va5p5gifl5gangbqvrc54igkii

Honeycomb networks: Topological properties and communication algorithms

I. Stojmenovic
1997 IEEE Transactions on Parallel and Distributed Systems  
Vertex and edge symmetric honeycomb torus network is obtained by adding wraparound edges to the honeycomb mesh.  ...  The average distance in honeycomb torus with n nodes is proved to be approximately 0.54 n .  ...  n 0.82 n torus 4 n 4 n 2 n hexagonal torus 6 0.58 n 3.46 n 4.61 n honeycomb torus 3 0.81 n 2.45 n 2.04 n honeycomb rhombic mesh 3 2.83 n 8.49 n 0.71 n honeycomb square mesh  ... 
doi:10.1109/71.629486 fatcat:thpowr3xnzdlfeacs6eskcnj6i

Ring embedding in faulty honeycomb rectangular torus

Hsun-Jung Cho, Li-Yen Hsu
2002 Information Processing Letters  
The honeycomb rectangular torus HReT(m, n) is recognized as another attractive alternative to existing torus interconnection networks in parallel and distributed applications.  ...  Recently, Cho and Hsu [5] have generalized the honeycomb torus into generalized honeycomb torus, and some generalized honeycomb tori are proved to be hamiltonian.  ...  Its topological properties and its generalization are studied by Parhami and Kwai [9] . Some applications of the honeycomb rectangular torus are studied in [4] .  ... 
doi:10.1016/s0020-0190(02)00310-1 fatcat:4vfcn7s53nggloumzt7yczbcce

Structural properties of Cayley digraphs with applications to mesh and pruned torus interconnection networks

Wenjun Xiao, Behrooz Parhami
2007 Journal of computer and system sciences (Print)  
We discuss applications of these results to well-known and useful interconnection networks such as hexagonal and honeycomb meshes as well as certain classes of pruned tori.  ...  Honeycomb torus networks The authors of [11] studied the honeycomb torus network as a pruned 2D torus.  ...  Thus the honeycomb torus is a homomorphic image of the infinite honeycomb network by Theorem 1.  ... 
doi:10.1016/j.jcss.2007.02.010 fatcat:crlz7ovdtngxnjufevqvi3i56y

Target set selection problem for honeycomb networks [article]

Chun-Ying Chiang, Liang-Hao Huang, Hong-Gwa Yeh
2012 arXiv   pre-print
set for different kinds regular graphs in the class of honeycomb networks  ...  We are interested in finding an optimal target set for the well-known class of honeycomb networks under an important threshold function called strict majority threshold, where θ(v)= (d_G(v)+1)/2 for each  ...  The generalized honeycomb rectangular torus (or generalized honeycomb torus), denoted by GHT(m, n, d) and proposed by Cho and Hsu [10] , is the graph with the vertex set {(i, j) : 0 ≤ i < m, 0 ≤ j < n  ... 
arXiv:1203.0666v1 fatcat:3t2475ml3fceph3ie6p6a7xlvm

Further Properties of Cayley Digraphs and Their Applications to Interconnection Networks [chapter]

Wenjun Xiao, Behrooz Parhami
2006 Lecture Notes in Computer Science  
We discuss applications of these results to well-known and useful interconnection networks such as hexagonal and honeycomb meshes.  ...  In this short communication, we extend the known relationships between Cayley digraphs and their subgraphs and coset graphs with respect to subgroups and obtain some general results on homomorphism and  ...  In [8] , the authors studied the honeycomb torus network as a pruned 2D torus. They also proved that the honeycomb torus network is a Cayley graph, without explicating its associated group.  ... 
doi:10.1007/11750321_18 fatcat:fvldaotpg5eedpjwlqv4hwfvm4

Diameter of parallelogramic honeycomb torus

Xiaofan Yang, G.M. Megson, Yuanyan Tang, D.J. Evans
2005 Computers and Mathematics with Applications  
In this paper, we establish an expression for the diameter of a general parallelogramic honeycomb torus, which extends a known result about rhombic honeycomb torus.  ...  Cho [3] introduced the notion of generalized honeycomb tori, which includes the aforementioned three classes of honeycomb tori as special cases.  ...  In particular, PHT,,~ is called a rhombic honeycomb torus of order n and is denoted by RoHT,~.  ... 
doi:10.1016/j.camwa.2005.01.029 fatcat:kqpe5jl4ljdc5fje2vzzchrbne

Page 370 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews  
A special case of this general form is the Finite Version (Theorem 2), followed by the Honeycomb Conjecture on a Torus (Theorem 3).  ...  Yet this is the version that implies the general result. Theorem 3 includes uniqueness of the optimal solution: the regular hexagonal honeycomb on the torus.  ... 

On Three Constructions of Nanotori

Vesna Andova, Pavel Dimovski, Martin Knor, Riste Škrekovski
2020 Mathematics  
honeycomb tori.  ...  four parameters used mostly in chemistry and physics after the discovery of fullerene molecules, and one with three parameters used in interconnecting networks of computer science known under the name generalized  ...  Figure 5 . 5 Generalized honeycomb torus GHT (3, 8, 7) . Proposition 3 . 3 The generalized honeycomb torus, GHT(a, b, c), has exactly ab vertices and ab/2 hexagons.  ... 
doi:10.3390/math8112036 fatcat:6tdgu6vcabbpdcf3g3upbtznse

One-to-One Embedding between Honeycomb Mesh and Petersen-Torus Networks

Jung-Hyun Seo, Hyun Sim, Dae-Heon Park, Jang-Woo Park, Yang-Sun Lee
2011 Sensors  
Petersen-Torus has been designed recently, and the honeycomb mesh has already been designed as a well-known interconnection network.  ...  The proposed one-to-one embedding is applied so that processor throughput can be minimized when the honeycomb mesh algorithm runs in the Petersen-Torus.  ...  The proposed embedding algorithm can be available in both a wormhole routing system and a store-and-forward routing system by embedding the generally known honeycomb mesh network in Petersen-Torus with  ... 
doi:10.3390/s110201959 pmid:22319392 pmcid:PMC3274048 fatcat:ctugknyw5ng7th4oloraiivfbi
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