Connected Outer-Hop Independent Dominating Sets in Graphs Under Some Binary Operations

Abstract

Let $G$ be a connected graph. A set $D\subseteq V(G)$ is called a connected outer-hop independent dominating if
$D$ is a connected dominating set and $V(G)\ D$ is a hop independent set in $G$, respectively. The minimum
cardinality of a connected outer-hop independent dominating set in $G$, denoted by $\gamma_{c}^{ohi}(G)$, is
called the connected outer-hop independent domination number of $G$. In this paper, we introduce and investigated
the concept of connected outer-hop independent domination in a graph. We show that the connected outer-hop
independent domination number and connected outer-independent domination number of a graph are incomparable.
In fact, we find that their absolute difference can be made arbitrarily large. In addition, we characterize
connected outer-hop independent dominating sets in graphs under some binary operations. Furthermore, these
results are used to give exact values or bounds of the parameter for these graphs.