Remarks on hyperenergetic circulant graphs Original Research Article

We first settle an open problem of Balakrishnan from Linear Algebra Appl. 387 (2004) 287–295. Further, if image, n set membership, variant N, k1 < k2 < cdots, three dots, centered < km < n/2, ki set membership, variant 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-45 degree rule{u} except u ± ki (mod n), i = 1, 2, …, m, we show that for any given k1 < k2 < cdots, three dots, centered < km almost all circulant graphs image are hyperenergetic.