# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

B. Pahlavsay, E. Palezzato, M. Torielli

Title:

3-tuple total domination number of rook's graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-09-11, Revised: 2019-03-11, Accepted: 2019-06-13, https://doi.org/10.7151/dmgt.2242

Abstract:

A $k$-tuple total dominating set ($k$TDS) of a graph $G$ is a set $S$ of vertices in which every vertex in $G$ is adjacent to at least $k$ vertices in $S$. The minimum size of a $k$TDS is called the $k$-tuple total dominating number and it is denoted by $\gamma_{\times k,t}(G)$. We give a constructive proof of a general formula for $\gamma_{\times 3, t} (K_n \Box K_m)$.

Keywords:

$k$-tuple total domination, Cartesian product of graphs, rook's graph, Vizing's conjecture