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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