doiSerbia

Equienergetic chemical trees

Brankov Vladimir (Department of Mathematics, Faculty of Science, University of Niš, Niš)
Stevanović Dragan P. (Department of Mathematics, Faculty of Science, University of Niš, Niš)
Gutman Ivan (Faculty of Science, University of Kragujevac, Kragujevac, Serbia and Montenegro)

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.

Keywords: energy of graph, total ¶-electron energy, chemical trees, equienergetic graphs