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Network vulnerability parameter and results on two surfaces
Author(s) -
Gao Wei,
Chen Yaojun,
Wang Yiqiao
Publication year - 2021
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22464
Subject(s) - conjecture , toughness , upper and lower bounds , graph , surface (topology) , vulnerability (computing) , perspective (graphical) , combinatorics , computer science , mathematics , discrete mathematics , materials science , geometry , composite material , mathematical analysis , computer security
Isolation toughness is a vital parameter to evaluate the vulnerability of computer networks. In specific network designing stage, it is necessary to find the lower bound of the isolated toughness, and strive to build a network that meets the stability requirements with the least cost. Gao et al. 1 conjectured that if a graph G with κ ( G ) ≥ 3 m + 1 2 satisfies I ( G ) > 7 m + 5 4 m + 4or I ′ ( G ) > 7 m + 5 4 m + 2 , then G is a ( P ≥ 3 , m ) ‐factor deleted graph. It's proved that this conjecture holds. However, it is found that as the connectivity changes, the tight lower bound of isolated toughness for ( P ≥ 3 , m ) ‐factor deleted graphs will change as well. Therefore, we propose a new perspective to look into this problem and introduce the concepts of isolated toughness ( P ≥ 3 , m ) factor deleted surface and isolated toughness variant ( P ≥ 3 , m ) factor deleted surface, where the result of the original conjecture is only a cross‐section on surfaces. The main contribution in this paper is to determine the concrete expression of these two surfaces.