Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (3): 221-234.doi: 10.13371/j.cnki.chin.q.j.m.2024.03.001

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Italian Domination of Strong Product of Two Paths

  

  1. Computer College, Qinghai Normal University, Xining 810000, China
  • Received:2023-07-18 Online:2024-09-30 Published:2024-09-30
  • Contact: LI Feng (1981-), male, native of Wuhu, Anhui, Ph.D., professor, engages in combinatorial networks and optimization, network optimization theory and algorithms, etc. E-mail:li2006369@126.com
  • About author:WEI Li-yang (2000-), female, native of Lanzhou, Gansu, master’s degree, engages in combinatorial network theory and optimization; LI Feng (1981-), male, native of Wuhu, Anhui, Ph.D., professor, engages in combinatorial networks and optimization, network optimization theory and algorithms, etc.
  • Supported by:
    Supported by the National Natural Science Foundation of China (Grant No. 11551002); The Natural Science Foundation of Qinghai Province (Grant No. 2019-ZJ-7093).

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Abstract: The domination problem of graphs is an important issue in the field of graph theory. This paper mainly considers the Italian domination number of the strong product between two paths. By constructing recursive Italian dominating functions, the upper bound of its Italian domination number is obtained, and then a partition method is proposed to prove its lower bound. Finally, this paper yields a sharp bound for the Italian domination number of the strong product of paths.

Key words: Partitioning approach, Roman domination, Italian domination, Strong product

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