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ISOLATED SCATTERING NUMBER OF SPLIT GRAPHS AND GRAPH PRODUCTS

Part of: Operations research and management science Graph theory Circuits, networks

Published online by Cambridge University Press:  12 April 2017

FENGWEI LI ,
QINGFANG YE  and
XIAOYAN ZHANG
FENGWEI LI*
Affiliation:
Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 312000, PR China email fengwei.li@hotmail.com, fqy-y@163.com
QINGFANG YE
Affiliation:
Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 312000, PR China email fengwei.li@hotmail.com, fqy-y@163.com
XIAOYAN ZHANG
Affiliation:
School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210023, PR China email zhangxiaoyan@njnu.edu.cn
*
✉fengwei.li@hotmail.com
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Abstract

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Computer or communication networks are so designed that they do not easily get disrupted under external attack. Moreover, they are easily reconstructed when they do get disrupted. These desirable properties of networks can be measured by various parameters, such as connectivity, toughness and scattering number. Among these parameters, the isolated scattering number is a comparatively better parameter to measure the vulnerability of networks. In this paper we first prove that for split graphs, this number can be computed in polynomial time. Then we determine the isolated scattering number of the Cartesian product and the Kronecker product of special graphs and special permutation graphs.

Keywords

isolated scattering numbersplit graphsubmodular functionKronecker productCartesian product

MSC classification

Primary: 90B18: Communication networks
Secondary: 94C15: Applications of graph theory 05C40: Connectivity 05C90: Applications
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 3-4 , April 2017 , pp. 350 - 358
Copyright
© 2017 Australian Mathematical Society 

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