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On a measure of communication network vulnerability
Author(s) -
Exoo Geoffrey
Publication year - 1982
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.3230120405
Subject(s) - mathematical proof , measure (data warehouse) , mathematics , vulnerability (computing) , line (geometry) , real line , graph , discrete mathematics , computer science , combinatorics , data mining , geometry , computer security
A measure of communication network vulnerability was studied in a recent article by Boesch, Harary, and Kabell. The persistence (line persistence) is the minimum number of points (lines) whose removal from a graph increases its diameter. Their approach differed from earlier work on this topic in that they examined the analogs of Menger's theorem for these invariants. A result of Lovász, Neumann‐Lara, and Plummer is used to prove modified versions of their theorems (the original proofs are incorrect). Some related problems are also solved, including one posed by Hartman and Rubin.