Diameter Formula for a Special 3D Hexagonal Torus

doi:10.3778/j.issn.1002-8331.1807-0199

Computer Engineering and Applications ›› 2019, Vol. 55 ›› Issue (13): 119-122.DOI: 10.3778/j.issn.1002-8331.1807-0199

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Diameter Formula for a Special 3D Hexagonal Torus

ZHONG Wei1，2, LIU Rihua3, CHEN Baoxing1，2

1.School of Computer Science, Minnan Normal University, Zhangzhou, Fujian 363000, China
2.Key Laboratory of Data Science and Intelligence Application, Fujian Province University, Zhangzhou, Fujian 363000, China
3.Department of Mathematics and Computer Science, Nanchang Normal University, Nanchang 330032, China

Online:2019-07-01 Published:2019-07-01

一类特殊三维六度环面网络的直径公式

钟玮1，2，刘日华3，陈宝兴1，2

1.闽南师范大学计算机学院，福建漳州 363000
2.数据科学与智能应用福建省高等学校重点实验室，福建漳州 363000
3.南昌师范学院数学与计算机科学系，南昌 330032

Abstract

Abstract: Hexagonal mesh and hexagonal torus network has been very widely used in chemistry, computer graphics and peak nest mobile communications and other fields. The 3D torus is natural extension of the torus. In this paper, for the unsolved problem of the 3D hexagonal torus Cayley network model proposed by Zhang Zhen et al, the diameter formula of the special 3D hexagonal torus Cayley network is given and proved in detail.

Key words: 3D hexagonal torus, Cayley graph, diameter formula

摘要： 六度网孔网络和六度环面网络在化学、计算机图形学和峰巢移动通信等领域都得到了十分广泛的应用。三维环面是二维环面的自然性推广。该文针对张震等人所提出的三维六度环面Cayley图网络模型的未解问题，给出了一类特殊三维六度环面网络的直径公式，并给予了详细的证明。

关键词: 三维六度环面网络, Cayley图, 直径公式

ZHONG Wei1，2, LIU Rihua3, CHEN Baoxing1，2. Diameter Formula for a Special 3D Hexagonal Torus[J]. Computer Engineering and Applications, 2019, 55(13): 119-122.

钟玮1，2，刘日华3，陈宝兴1，2. 一类特殊三维六度环面网络的直径公式[J]. 计算机工程与应用, 2019, 55(13): 119-122.

[1]	ZHONG Wei, CHEN Baoxing. Fast algorithm of calculating diameter for Bi-Cayley graph with 4 degrees on cyclic group [J]. Computer Engineering and Applications, 2015, 51(14): 67-71.
[2]	ZHAO Cheng-gui. Unified formulation of several multistage interconnection networks [J]. Computer Engineering and Applications, 2010, 46(36): 118-121.
[3]	WEI Chang-ming¹，LIU Hao²，ZHANG Lian-ming^1，2. Small world network model based on Cayley graph [J]. Computer Engineering and Applications, 2009, 45(28): 99-101.
[4]	SHI Hai-zhong,LU Jian-bo. On conjectures of interconnection networks [J]. Computer Engineering and Applications, 2008, 44(31): 112-115.

Diameter Formula for a Special 3D Hexagonal Torus

一类特殊三维六度环面网络的直径公式

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