Some eigenvalue properties in graphs (conjectures of Graffiti -- II)
Several bounds on the largest eigenvalue of the adjacency matrix of a graph are presented. Some additional inequalities relate eigenvalues and some other graph invariants. As a consequence, numerous conjectures of the computer program Graffiti are settled. On the other hand, 49 (forty nine) conjectures of the same program are disproved by means of counterexamples (usually infinite families). Concerning the settled and eliminated conjectures, it is not clear to the reviewer what is their mathematical value. Nevertheless, it is to be stressed that a paper containing many proved and disproved conjectures is very difficult to find.
scientific article; zbMATH DE number 428314