20.500.12556/RUP-22291 Tight upper bounds for the p-anionic Clar number of fullerenes Stroge zgornje meje za p-anionsko Clarjevo število fulerenov A 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. chemical graph theory anionic Clar number fullerenes kemijska teorija grafov anionsko Clarjevo število fulereni true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-12-21 23:08:29 2025-12-21 23:08:29 2026-01-05 12:13:12 0000-00-00 00:00:00 2026 0 0 38 str. no. 1, [article no.] P1.07 Vol. 26 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-11-26 51 1855-3974 10.26493/1855-3974.3282.6ea AMC_Slobodin,_Myrvold,_MacGillivray,_Fowler_2026.pdf AMC_Slobodin,_Myrvold,_MacGillivray,_Fowler_2026.pdf 1 F1E903EF8BFA7995AC4D77A67CBA3379 e42e9de33f2c156d94b400213233139b9062be2a6b0097fb18d91c140086648f 4ba3701b-deba-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32372 Založba Univerze na Primorskem 0 0 0