When is NEPS of graphs connected?

Abstract

We give the sufficient and necessary condition for the connectedness of non-complete extended p-sum (NEPS) of connected graphs, and we find the number of components of NEPS when it is disconnected. We show that the components of NEPS are mutually isomorphic and isomorphic to NEPS of the same non-bipartite factors and several copies of K2 in the case that K2 is the only bipartite factor of NEPS.