Bounds on the Domination Numbers of δ-Complement Graphs
Discuss this preprint
Start a discussion What are Sciety discussions?Listed in
This article is not in any list yet, why not save it to one of your lists.Abstract
This study examines the δ-complements of graphs—a specific type of graph complement whose adjacency depends on the adjacency of the vertices with identical degrees in the original graph. More specifically, we study this type of complement regarding the domination number. We provide sharp Nordhaus-Gaddum-type bounds on the domination number of a graph and its δ-complement. We also provide sharp bounds on the domination numbers of the δ-complements of joined graphs and Cartesian product graphs.