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Reliability of interconnection networks modeled by Cartesian product digraphs
Author(s) -
Yang Chao,
Xu JunMing
Publication year - 2008
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20231
Subject(s) - cartesian product , degree (music) , interconnection , enhanced data rates for gsm evolution , combinatorics , reliability (semiconductor) , product (mathematics) , mathematics , vertex connectivity , cartesian coordinate system , computer science , order (exchange) , discrete mathematics , graph , physics , computer network , telecommunications , geometry , vertex (graph theory) , power (physics) , finance , quantum mechanics , acoustics , economics
We determine that the connectivity and the edge‐connectivity of the Cartesian product G 1 × G 2 of two strongly connected and finite digraphs G 1 and G 2 are equal to min{ n 1 κ 2 , n 2 κ 1 ,δ + 1+ δ + 2 , δ − 1+ δ − 2 } and min{ n 1 λ 2 , n 2 λ 1 , δ + 1+ δ + 2 , δ − 1+ δ − 2 }, respectively, where n i , κ i , λ i , δ + i , δ − iare the order, the connectivity, the edge‐connectivity, the minimum out‐degree and the minimum in‐degree of G i , respectively, for i = 1, 2. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008
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