TY - JOUR
AU - Manditong, Jahiri
AU - Hassan, Javier
AU - Laja, Ladznar S.
AU - Laja, Amy A.
AU - Mohammad, Nurijam Hanna M.
AU - Kamdon, Sisteta U.
PY - 2023/07/30
Y2 - 2023/11/29
TI - Connected Outer-Hop Independent Dominating Sets in Graphs Under Some Binary Operations
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 16
IS - 3
SE -
DO - 10.29020/nybg.ejpam.v16i3.4766
UR - https://ejpam.com/index.php/ejpam/article/view/4766
SP - 1817-1829
AB - <pre>Let $G$ be a connected graph. A set $D\subseteq V(G)$ is called a connected outer-hop independent dominating if<br /> $D$ is a connected dominating set and $V(G)\ D$ is a hop independent set in $G$, respectively. The minimum<br /> cardinality of a connected outer-hop independent dominating set in $G$, denoted by $\gamma_{c}^{ohi}(G)$, is<br /> called the connected outer-hop independent domination number of $G$. In this paper, we introduce and investigated<br /> the concept of connected outer-hop independent domination in a graph. We show that the connected outer-hop <br />independent domination number and connected outer-independent domination number of a graph are incomparable.<br /> In fact, we find that their absolute difference can be made arbitrarily large. In addition, we characterize<br /> connected outer-hop independent dominating sets in graphs under some binary operations. Furthermore, these <br />results are used to give exact values or bounds of the parameter for these graphs.</pre>
ER -