Italian Domination of Strong Product of Two Paths

WEI Li-yang, LI Feng

doi:10.13371/j.cnki.chin.q.j.m.2024.03.001

Chinese Quarterly Journal of Mathematics >

2024 , Vol. 39 >Issue 3: 221 - 234

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.03.001

Italian Domination of Strong Product of Two Paths

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Computer College, Qinghai Normal University, Xining 810000, China

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.

Received date: 2023-07-18

Online published: 2024-09-30

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

Cite this article

WEI Li-yang, LI Feng . Italian Domination of Strong Product of Two Paths[J]. Chinese Quarterly Journal of Mathematics, 2024 , 39(3) : 221 -234 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.001

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