数学季刊 ›› 2024, Vol. 39 ›› Issue (3): 221-234.doi: 10.13371/j.cnki.chin.q.j.m.2024.03.001

• •    下一篇

两条路径强乘积图的意大利控制数

  

  1. Computer College, Qinghai Normal University, Xining 810000, China
  • 收稿日期:2023-07-18 出版日期:2024-09-30 发布日期:2024-09-30
  • 通讯作者: 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
  • 作者简介: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.
  • 基金资助:
    Supported by the National Natural Science Foundation of China (Grant No. 11551002); The Natural Science Foundation of Qinghai Province (Grant No. 2019-ZJ-7093).

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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摘要： 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.

关键词: Partitioning approach, Roman domination, Italian domination, Strong product

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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