@article{Li2023, 
author = {Linyu Li and Jun Yue and Xia Zhang},
title = {Double total domination number of Cartesian product of paths},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {9506-9519},
keywords = {dominating sets, total domination, double total domination, Cartesian product, paths},
url = {https://www.sciopen.com/article/10.3934/math.2023479},
doi = {10.3934/math.2023479},
abstract = {A vertex set    S of a graph    G is called a double total dominating set if every vertex in    G has at least two adjacent vertices in    S. The double total domination number        γ          ×      2      ,      t        (  G  ) of    G is the minimum cardinality over all the double total dominating sets in    G. Let    G  ◻  H denote the Cartesian product of graphs    G and    H. In this paper, the double total domination number of Cartesian product of paths is discussed. We determine the values of        γ          ×      2      ,      t        (      P    i    ◻      P    n    ) for    i  =  2  ,  3, and give lower and upper bounds of        γ          ×      2      ,      t        (      P    i    ◻      P    n    ) for    i  ≥  4.}
}