Naslov
Cubic ramapolyhedra with face size no larger than 6

Autori
Dutour Sikirić, Mathieu ; Fowler, Patrick

Izvornik
Journal of mathematical chemistry (0259-9791) 49 (2011), 4; 843-858

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
graph theory; eigenvalues; ramanujan graphs; polyhedra

Sažetak
A k-regular graph is Ramanujan if its second largest eigenvalue (by magnitude) has magnitude less than or equal to 2sqrt(k-1). Exhaustive search up to the bound of 138 vertices, derived from Spielman and Teng's work on graph partitioning, finds all cubic polyhedral Ramanujan graphs with positive curvature, i.e., with face sizes no larger than 6. Of all such polyhedra, those with face sizes 5 or 6, i.e., fullerenes, give the largest known examples of cubic Ramanujan polyhedra (with 84 vertices). We also consider the notions of negative and positive Ramanujan graphs, as those without eigenvalues in the respective open intervals (-k, -2sqrt{;k-1};) and (2\sqrt{;k-1};k). Our results give the full list of positive cubic polyhedral Ramanujan graphs with positive curvature but for negative Ramanujan graphs we have only a finiteness theorem and a conjectured complete list.

Izvorni jezik
Engleski

Znanstvena područja
Kemija

POVEZANOST RADA