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http://dx.doi.org/10.3745/KIPSTA.2011.18A.6.225

Hamiltonian Paths in Restricted Hypercube-Like Graphs with Edge Faults  

Kim, Sook-Yeon (한경대학교 컴퓨터공학과)
Chun, Byung-Tae (한경대학교 웹정보공학과)
Publication Information
The KIPS Transactions:PartA / v.18A, no.6, 2011 , pp. 225-232 More about this Journal
Abstract
Restricted Hypercube-Like (RHL) graphs are a graph class that widely includes useful interconnection networks such as crossed cube, Mobius cube, Mcube, twisted cube, locally twisted cube, multiply twisted cube, and generalized twisted cube. In this paper, we show that for an m-dimensional RHL graph G, $m{\geq}4$, with an arbitrary faulty edge set $F{\subset}E(G)$, ${\mid}F{\mid}{\leq}m-2$, graph $G{\setminus}F$ has a hamiltonian path between any distinct two nodes s and t if dist(s, V(F))${\neq}1$ or dist(t, V(F))${\neq}1$. Graph $G{\setminus}F$ is the graph G whose faulty edges are removed. Set V(F) is the end vertex set of the edges in F and dist(v, V(F)) is the minimum distance between vertex v and the vertices in V(F).
Keywords
Restricted Hypercube-Like Graph; Crossed Cube; Mobius Cube; Mcube; Twisted Cube; Locally Twisted Cube; Multiply Twisted Cube; Generalized Twisted Cube; Fault Tolerance; Hamiltonian Path; Hamiltonian Connected Graph;
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