Remarks on hyperenergetic circulant graphs

AbstractWe first settle an open problem of Balakrishnan from Linear Algebra Appl. 387 (2004) 287–295. Further, if Ci¯(n,k1,k2,⋯,km), n∈N, k1<k2<⋯<km<n/2, ki∈N for i=1,2,…,m, denotes a circulant graph with the vertex set V={0,1,…,n−1} such that a vertex u is adjacent to all vertices of V⧹{u} except u±ki(modn), i=1,2,…,m, we show that for any given k1<k2<⋯