Tight upper bounds for the p-anionic Clar number of fullerenesSlobodin, Aaron (Avtor) Myrvold, Wendy (Avtor) MacGillivray, Gary (Avtor) Fowler, Patrick W. (Avtor) chemical graph theoryanionic Clar numberfullerenesA fullerene is an all-carbon molecule with a polyhedral structure where each atom is bonded to three other atoms and each face is either a pentagon or a hexagon. Fullerenes correspond to 3-regular planar graphs whose faces have sizes 5 or 6. The p-anionic Clar number C_(p)(G) of a fullerene G is equal to p + h, where h is maximized over all choices of p + h independent faces (exactly p pentagons and h hexagons) the deletion of whose vertices leave a graph with a perfect matching. This definition is motivated by the chemical observation that pentagonal rings can accommodate an extra electron, so that the pentagons of a fullerene with charge −p, compete with the hexagons to host ‘Clar sextets’ of six electrons, and pentagons will preferentially acquire the p excess electrons of the anion. Tight upper bounds are established for the p-anionic Clar number of fullerenes for p > 0. The upper bounds are derived via graph theoretic arguments and new results on minimal cyclic-k-edge cutsets in IPR fullerenes (fullerenes that have all pentagons pairwise disjoint). These bounds are shown to be tight by infinite families of fullerenes that achieve them.Založba Univerze na Primorskem20262025-12-21 23:08:29Članek v reviji22291UDK: 51eISSN: 1855-3974DOI: 10.26493/1855-3974.3282.6easl