On the construction of most reliable networks

Authors:
Hanyuan Deng;Jianer Chen;Qiaoliang Li;Rongheng Li;Qiju Gao
Affiliations:
Department of Mathematics, Hunan Normal University, ChangSha, Hunan 410081, People's Republic of China;College of Information Engineering, Central-South University of Technology, ChangSha, Hunan 410083, People's Republic of China;Department of Mathematics, Hunan Normal University, ChangSha, Hunan 410081, People's Republic of China;Department of Mathematics, Hunan Normal University, ChangSha, Hunan 410081, People's Republic of China;Department of Mathematics, Hunan Normal University, ChangSha, Hunan 410081, People's Republic of China
Venue:
Discrete Applied Mathematics
Year:
2004

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Abstract

The construction of most reliable networks is investigated. In particular, the study of restricted edge connectivity shows that general Harary graphs are max λ-min mi for all i=λ, λ+1,....2λ- 3. As a consequence, this implies that for each pair of positive integers n and e, there is a graph of n vertices and e edges that is max λ-min mi for all i= λ,λ + 1,....2λ - 3. General Harary graphs that are max λ-min mi for all i= λ, λ + 1,.... 2λ - 2 are also constructed.