Journal
| Title | On independent transversal dominating sets in graphs Posted by Ferdinand Jamil |
| 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 | https://doi.org/10.29020/nybg.ejpam.v14i1.3904 |
| URL | http://www.ejpam.com |