Fault-Tolerant Hypercubes with Small Degree
Toshinori Yamada, Shuichi Ueno · 1998
For a given N-vertex graph. H, a graph G obtained from H by adding t vertices a,nd some edges is called a t-FT (t-fault-toleran,t) graph. for H if even after delet-in.g any t vertices from G, the remaining graph con-tains H as a subgraph. For an N-vertex hypercube QN, a t-FT graph with an, optimal number O(tN +t2) of added edges and maximum degree of O(N + t), and a, t-FT graph zuith O(tN log N) added edges and max-imum degree of O(t 1ogN) have been known. In this paper, we introduce some t-FT graphs for QN with an optimal number O(tN + t2) of added edges and small maximum degree. In particular, we show a t-FT graph, for QN with 2ctN+ct2 v ’ added edges and max- c> imum degree of 0 (,0g~~2 N) + 4ct 1