# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

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

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

A.C. Martínez, I. Peterin, I.G. Yero

Title:

Independent transversal total domination versus total domination in trees

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-06-06, Revised: 2018-09-11, Accepted: 2018-09-12, https://doi.org/10.7151/dmgt.2200

Abstract:

A subset of vertices in a graph $G$ is a total dominating set if every vertex in $G$ is adjacent to at least one vertex in this subset. The total domination number of $G$ is the minimum cardinality of any total dominating set in $G$ and is denoted by $\gamma_t(G)$. A total dominating set of $G$ having nonempty intersection with all the independent sets of maximum cardinality in $G$ is an independent transversal total dominating set. The minimum cardinality of any independent transversal total dominating set is denoted by $\gamma_{tt}(G)$. Based on the fact that for any tree $T$, $\gamma_{t}(T)\le \gamma_{tt}(T)\le \gamma_{t}(T)+1$, in this work we give several relationships between $\gamma_{tt}(T)$ and $\gamma_{t}(T)$ for trees $T$ which are leading to classify the trees which are satisfying the equality in these bounds.

Keywords:

independent transversal total domination number, total domination number, independence number, trees