JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (3): 88-95.doi: 10.6040/j.issn.1671-9352.0.2020.355

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General p-neighbor scattering number of graphs

YANG Xue, WEI Zong-tian, JIANG Shu-yan   

  1. Department of Mathematics, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China
  • Published:2021-03-16

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Abstract: The study of network neighbor invulnerability originated from spy networks. The particularity is that if a vertex has been destroyed, its adjacent vertices will be useless as a whole. However, the most likely situation is that if a vertex has been destroyed, its adjacent vertices will be failed with some probability p. Based on this idea, the concept of general p-neighbor scattering number is proposed. The p-neighbor scattering number formula of some special graphs and line graphs are given. The accuracy of network neighbor invulnerability measure is illustrated by the analysis of the relationship of p and the general p-neighbor scattering number.

Key words: graph, vertex-neighbor-scattering number, failure probability, general p-neighbor scattering number, invulnerability

CLC Number: 

  • O157.5
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