generalized hypercube
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2021 ◽  
Vol 400 ◽  
pp. 126090
Author(s):  
Ruichao Niu ◽  
Min Xu ◽  
Hong-Jian Lai


2020 ◽  
Vol 31 (3) ◽  
pp. 647-662 ◽  
Author(s):  
Guijuan Wang ◽  
Cheng-Kuan Lin ◽  
Jianxi Fan ◽  
Baolei Cheng ◽  
Xiaohua Jia


Author(s):  
Guijuan Wang ◽  
Cheng-Kuan Lin ◽  
Baolei Cheng ◽  
Jianxi Fan ◽  
Weibei Fan


2017 ◽  
Vol 28 (07) ◽  
pp. 915-929 ◽  
Author(s):  
Lili Guo ◽  
Xi Wang ◽  
Cheng-Kuan Lin ◽  
Jingya Zhou ◽  
Jianxi Fan

The generalized hypercube is a highly-connective network proposed by Bhuyan and Agrawal. In this paper, we study the restricted connectivity and fault-free unicast algorithm in the generalized hypercube. Firstly, we prove that the restricted connectivity of a [Formula: see text]-dimensional generalized hypercube [Formula: see text] is [Formula: see text], where [Formula: see text] denotes the connectivity of [Formula: see text] and [Formula: see text] max [Formula: see text], under the condition that each vertex has at least one fault-free neighbor. It is almost twice the traditional connectivity of [Formula: see text]. Furthermore, we present an [Formula: see text] fault-free unicast algorithm in the generalized hypercube.



2016 ◽  
Vol 16 (03n04) ◽  
pp. 1650008
Author(s):  
YAPING MAO ◽  
ZHIWEI GUO ◽  
NAN JIA ◽  
HE LI

A linear k-forest is a forest whose components are paths of length at most k. The linear k-arboricity of a graph G, denoted bylak(G), is the least number of linear k-forests needed to decompose G. Recently, Zuo, He, and Xue studied the exact values of the linear(n−1)-arboricity of Cartesian products of various combinations of complete graphs, cycles, complete multipartite graphs. In this paper, for general k we show thatmax{lak(G),lal(H)}≤lamax{k,l}(G□H)≤lak(G)+lal(H)for any two graphs G and H. Denote byG∘H, G×HandG⊠Hthe lexicographic product, direct product and strong product of two graphs G and H, respectively. For any two graphs G and H, we also derive upper and lower bounds oflak(G∘H),lak(G×H)andlak(G⊠H)in this paper. The linear k-arboricity of a 2-dimensional grid graph, a r-dimensional mesh, a r-dimensional torus, a r-dimensional generalized hypercube and a hyper Petersen network are also studied.





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