JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (4): 102-108.doi: 10.6040/j.issn.1671-9352.0.2024.245

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Analysis of network invulnerability based on the multi-fire source burning connectivity

BAI Yuerong, WEI Zongtian, WANG Deli   

  1. Department of Mathematics, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China
  • Published:2026-04-08

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Abstract: The multi-fire source burning connectivity is given for several types of Cartesian product graphs. The relationship between multi-fire source burning connectivity and graph structure is analyzed, and the inverse problem of multi-fire source burning connectivity is proposed, that is, given a positive number m, determine the fire source such that the graph is burned as disconnected or empty within m steps at most, and contains as few vertices as possible(the minimum fire source). Finally, an algorithm of the minimum fire source of graphs is designed.

Key words: graph, invulnerability, multi-fire source burning connectivity, Cartesian product graphs, algorithm

CLC Number: 

  • O157.5
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