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Scattering number in graphs
Author(s) -
Zhang Shenggui,
Wang Ziguo
Publication year - 2001
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/1097-0037(200103)37:2<102::aid-net5>3.0.co;2-s
Subject(s) - scattering , graph , combinatorics , graph theory , mathematics , discrete mathematics , physics , quantum mechanics
The scattering number of a noncomplete connected graph G is defined by s ( G ) = max{ω( G − X ) − | X |: X ⊂ V ( G ), ω( G − X ) ≥ 2}, where ω( G − X ) denotes the number of components of the graph G − X . In this paper, we show that this parameter can be used to measure the vulnerability of a graph. To some extent, it represents a trade‐off between the amount of work done to damage the network and how badly the network is damaged. The relationship between the scattering number and some other parameters of a graph is discussed. Furthermore, we give the Nordhaus—Gaddum‐type result for scattering number. © 2001 John Wiley & Sons, Inc.