Carbon atoms self-assemble into the famous soccer-ball shaped Buckminsterfullerene (C(60)), the smallest fullerene cage that obeys the isolated-pentagon rule (IPR). Carbon atoms self-assemble into larger (n > 60 vertices) empty cages as well-but only the few that obey the IPR-and at least 1 small fullerene (n <or= 60) with adjacent pentagons. Clathrin protein also self-assembles into small full...

Besides the conventional D5h(8149)-C70 fullerene, there are a large number of C70 isomers that violate the isolated pentagon rule (IPR). However, these non-IPR C70 fullerenes have been less investigated owing to their low stabilities or high reactivities. In this study, we report for the first time the X-ray structure of an unconventional endohedral C70 fullerene, Sc2O@C2(7892)-C70. The combine...

We describe a new construction algorithm for the recursive generation of all non-isomorphic IPR fullerenes. Unlike previous algorithms, the new algorithm stays entirely within the class of IPR fullerenes, that is: every IPR fullerene is constructed by expanding a smaller IPR fullerene unless it belongs to a limited class of irreducible IPR fullerenes that can easily be made separately. The clas...

In this paper an algorithm for computing the Balaban and Randic indices of any simple connected graph was introduced. Also these indices were computed for IPR C80 fullerene isomers, Zigzag nanotubes and graphene by GAP program.

in this paper an algorithm for computing the balaban and randic indices of any simple connected graph was introduced. also these indices were computed for ipr c80 fullerene isomers, zigzag nanotubes and graphene by gap program.

in this paper pi, szeged and revised szeged indices of an infinite family of ipr fullereneswith exactly 60+12n carbon atoms are computed. a gap program is also presented that isuseful for our calculations.

In-situ ESR/UV-vis-NIR spectroelectrochemistry was implemented to probe the spin state of the radical cation of a non-IPR cluster-fullerene Sc(3)N@C(68), which represents the first study on the stable paramagnetic cation of an endohedral fullerene.

Endohedral metal carbides suggest an intriguing relationship to the growth mechanism of endohedral fullerenes; however, due to crystal quality requirements, only a half dozen of these have been characterized by single crystal X-ray diffraction. Likewise, few examples of nonisolated pentagon rule (non-IPR) endohedral fullerenes have been crystallographically characterized, beginning with Sc3N@C6...

We show that every pair of hexagons in a fullerene graph satisfying the isolated pentagon rule (IPR) forms a resonant pattern. This solves a problem raised by Ye et al. [SIAM J. Discrete Math. 23(2):2009, p. 1023–1044].

The most abundant fullerenes, C60 and C70, and all the pure-carbon fullerenes larger than C70 synthesized so far follow the isolated-pentagon rule (IPR). Fullerenes containing adjacent pentagons (APs) are less stable due to the additional strain. Surprisingly, recent experiments have shown that a few endohedral fullerenes, for which IPR structures are possible, hence expected to be the most sta...