Let A be the adjacency matrix of a simple graph G, and, λ1, λ2, . . . , λn , be the eigenvalues of the graph G. The energy of G is defined as the sum of absolute values of its eigenvaluesThe energy is a graph parameter stemming from the Hückel molecular orbital approximation for the.
The graph G is said to be hyperenergetic if its energy exceeds the energy of the complete graph Kn, or
equivalently if E(G) > 2n − 2. This concept was introduced first by Gutman
. graphs with maximum energy pertain to maximality stable π-electron systems. It has been proven
that for every n 8, there exists a hyperenergetic graph of order n.
A graph is called circulant if it is Cayley graph on the circulant group, i.e. its adjacency matrix is