Classification of borderenergetic chemical graphs and borderenergetic graphs of order 12

Péter Csikvári; Ivan Damnjanović; Marko Milošević; Ivan Stanković; Dragan Stevanović

Paper

Classification of borderenergetic chemical graphs and borderenergetic graphs of order 12

Abstract

The energy

of a simple graph

is the sum of absolute values of the eigenvalues of its adjacency matrix. A borderenergetic graph of order

is any noncomplete graph~

such that

. Here we combine two-phase computer-assisted search with theoretical arguments to show that there are only three borderenergetic chemical graphs, thus completing the earlier findings of Li, Wei and Zhu [MATCH Commun. Math. Comput. Chem. 77 (2017), 25-36]. We perform two-phase computer-assisted search to also find all

borderenergetic graphs of order~

, thereby correcting and extending the results from a previous search performed by Furtula and Gutman [Iranian J. Math. Chem. 8(4) (2017), 339-344].