A 3-restricted edge cut is an edge cut of a connected graph that separates this graph into components, each having an order of at least 3. The minimum size of all 3-restricted edge cuts of a graph is called its 3-restricted edge connectivity. This work determines the upper and lower bounds on the 3-restricted edge connectivity of replacement product graphs and presents sufficient conditions for replacement product graphs to be maximally 3-restricted edge connected. As a result, the 3-restricted edge connectivity of replacement product graphs of some special graphs are determined.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.