Groupe d’études et de recherche en analyse des décisions

# On the (1,2)-Spectral Spread of Fullerenes

## Dragan Stevanovic et Gilles Caporossi

Let G be a simple graph on n vertices with the eigenvalues (of an adjacency matrix) λ1 ≥ λ2 ≥ ... ≥ λn. For 1 ≤ i < jn, the (i,j)-spectral spread (or just (i,j)-spread) of G is defined as the difference λi - λj. The program Graffiti, developed by S. Fajtlowicz, posed the conjecture that the (1,2)-spread of fullerenes is at most 1. Here we prove this conjecture by using the interlacing theorem in an interesting manner and then extend this method to show that the dodecahedron has the largest (1,2)-spread amongst all fullerenes.

, 9 pages

Ce cahier a été révisé en décembre 2003