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

Let G be a connected graph. A set D subset of 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. The minimum cardinality among all connected outer-hop independent dominating sets in G, denoted by gamma(ohi)(c) (G), is called the connected outer-hop independent domination number of G. In this paper, we initiate the study and investigation of connected outer-hop independent domination in some families of graphs and graphs under some binary operations. We construct properties and determine its connections with other known concepts and parameters in graph theory. Moreover, we characterize this type of sets in the join and corona of two graphs, and we use these results to determine the exact values or bounds of the parameters of these graphs.