Polygonal chains with minimal energy

Abstract The energy of a graph G is defined as E ( G )=∑ i =1 p | λ i |, where λ i ( i =1,…, p ) are the eigenvalues of the adjacency matrix of G . We show that among all polygonal chains with polygons of 4 n −2 vertices ( n ⩾2), the linear polygonal chain has minimal energy.