Remarks on hyperenergetic circulant graphs

Abstract

We first settle an open problem of Balakrishnan from Linear Algebra Appl. 387 (2004) 287-295. Further, if Cī(n,k1,k2,⋯,km), n ∈ N, k1 < k2 < ... < km < n/2, k i ∈ 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 (mod n), i = 1, 2, ..., m, we show that for any given k1 < k2 < ... < k m almost all circulant graphs Cī(n,k1,k2,...,km) are hyperenergetic.