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Network reliability with node failures
Author(s) -
Liu Shaobin,
Cheng KamHoi,
Liu Xiaoping
Publication year - 2000
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/(sici)1097-0037(200003)35:2<109::aid-net2>3.0.co;2-n
Subject(s) - combinatorics , mathematics , discrete mathematics , cograph , graph , class (philosophy) , induced subgraph , indifference graph , split graph , chordal graph , 1 planar graph , computer science , artificial intelligence , vertex (graph theory)
Abstract Given a graph whose edges never fail but whose nodes fail independently of each other with a constant probability 1 − p , the reliability of a graph is defined to be the probability that the induced subgraph of the surviving nodes is connected. Let Ω ( n , m ) be the class of all graphs with n nodes and m edges. A graph G of Ω is said to be uniformly best in Ω, if for all choices of p , it is most reliable in the class of graphs, Ω. In this paper, the existing known set of uniformly best graphs is extended, and some closely related graphs are proved to be not the uniformly best graphs in their class. More precisely, we prove that for any positive integer b the complete tripartite graph K ( b , b + 1, b + 2) is uniformly best in its class Ω(3 b + 3, 3 b 2 + 6 b + 2), while the complete tripartite graphs K ( b , b + 1, b + i )( i > 2) are not the uniformly best in their classes Ω(3 b + i + 1, 3 b 2 + 2( i + 1) b + i ). © 2000 John Wiley & Sons, Inc.