The Exactness of the Total Domination Number in Semistrong Product of Two Path Graphs

Abeer M. M. Jaradat, Sahar A. Aleid, Maisa Khader and Anas Quedan

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-7

Abstract: In this paper, a constructive proof is provided to find the exact total domination number γt of the semistrong product of two path graphs Pmׯ_Pn, that is for m,n≥2, we have γtPmׯ_Pn=⌊1/2m⌋+⌈1/4m⌉−⌊1/4m⌋⋅⌈1/3n⌉, where the path graph Pm is a simple graph consisting of a sequence of m vertices connected consecutively by m−1 edges.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:7702582

DOI: 10.1155/ijmm/7702582

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