| Title |
On independent transversal dominating sets in graphs |
|
Authors |
D. Sevilleno and F. Jamil |
|
Publication date |
2021 |
|
Journal |
European Journal of Pure and Applied Mathematics |
| Volume |
14 |
| Issue |
1 |
| Pages |
149-163 |
| Publisher |
New York Business Global |
| Abstract |
A set $S subseteq V (G)$ is an independent transversal dominating set of a graph $G$ if $S$ is a dominating set of $G$ and intersects every maximum independent set of $G$. An independent
transversal dominating set which is a total dominating set is an independent transversal total dominating set. The minimum cardinality $gamma_{it}(G)$ (resp. $gamma_{itt}(G)$) of an independent transversal
dominating set (resp. independent transversal total dominating set) of $G$ is the independent transversal domination number (resp. independent transversal total domination number) of $G$. In
this paper, we show that for every positive integers $a$ and $b$ with $5 le a le b le 2a - 2$, there exists a connected graph $G$ for which $gamma_{it}(G) = a$ and $gamma_{itt}(G) = b$. We also study these two concepts in
graphs which are the join, corona or composition of graphs. |
| Index terms / Keywords |
independent transversal dominating set, independent transversal total dominating set, independent transversal domination number, independent transversal total domination number |
| DOI |
|
| URL |
|
Mindanao State
University - Iligan Institute of Technology