| Title: | Tight upper bounds for the p-anionic Clar number of fullerenes |
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| Authors: | ID Slobodin, Aaron (Author)
ID Myrvold, Wendy (Author)
ID MacGillivray, Gary (Author)
ID Fowler, Patrick W. (Author) |
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| Files: |  AMC_Slobodin,_Myrvold,_MacGillivray,_Fowler_2026.pdf (1,11 MB)
MD5: F1E903EF8BFA7995AC4D77A67CBA3379
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | 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. |
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| Keywords: | chemical graph theory, anionic Clar number, fullerenes |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 26.11.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 38 str. |
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| Numbering: | Vol. 26, no. 1, [article no.] P1.07 |
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| PID: | 20.500.12556/RUP-22291  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3282.6ea |
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| Publication date in RUP: | 21.12.2025 |
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| Views: | 191 |
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| Downloads: | 1 |
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