JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (6): 36-43.doi: 10.6040/j.issn.1671-9352.0.2021.330

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Weighted neighbor toughness of graphs

WENG Ting-ting, WEI Zong-tian   

  1. Department of Mathematics, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China
  • Published:2022-06-10

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Abstract: Introduced neighbor toughness into the weighted graph, and the concept of weighted neighbor toughness of the graph is proposed. On the basis of giving some basic graphs weighted neighbor toughness, the extreme value problem of weighted neighbor toughness of several types of graphs was focused. The results show that the parameter values are related to the structure of the graph, the size of the weights, and the way of weighting, so the invulnerability of the network can be described more accurately.

Key words: network invulnerability, weighted graph, weighted neighbor toughness, toughness

CLC Number: 

  • O157.5
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