Abstract. An edge-regular graph is a regular graph in which, for some λ, any two adjacent vertices have exactly λ common neighbors. This paper is about the existence and structure of edge-regular graphs with λ = 1 and about edge-regular graphs with λ > 1 which have local neighborhood structure analogous to that of the edge-regular graphs with λ = 1.
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.