Equienergetic chemical trees

Abstract

The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. Two graphs, G 1 and G 2 , are said to be equienergetic if E(G 1 ) = E(G 2 ). We report here the results of the search for pairs of equienergetic acyclic molecular graphs (chemical trees) with the same number n of vertices. There are very few such pairs. The smallest has n = 9 and pertains to 3,3-diethylpentane and 3-methyloctane. Among the chemical trees with n ≤ 18, only five more such pairs and a triplet were found.