When can the components of NEPS of connected bipartite graphs be almost cospectral? Original Research Article

We disprove the conjecture of Cvetkovi image posed in 1983 that the components of non-complete extended p-sum (NEPS) of connected bipartite graphs are almost cospectral (cf. D. Cvetkovi image , Publ. Inst. Math. (Beograd) 33 (47) (1983) 29–33). However, we do find the necessary condition for the components to be almost cospectral and we conjecture that it is also the sufficient condition. In the last part of the paper, we are interested in the question when NEPS of bipartite graphs is itself bipartite.