The Symmetric Division Eccentric Index of Two Infinite Classes of Fullerenes

Document Type : Research Paper

Authors

1 Department of Mathematics‎, ‎Salahaddin University-Erbil‎, ‎Kurdistan‎, ‎Iraq

2 Department of Mathematics‎, ‎Faculty of Science‎, ‎Shahid Rajaee Teacher Training University‎, ‎Tehran‎, ‎16785-163‎, ‎I‎. ‎R‎. ‎Iran

10.22052/ijmc.2025.255411.1998

Abstract

‎A fullerene graph is a 3-connected‎, ‎planar cubic graph where each face is either pentagonal or hexagonal‎. ‎This paper investigates the symmetric division eccentric index (\textit{SDE}) of fullerenes‎, ‎particularly focusing on two infinite classes $F_{10n}$ and $F_{12n}$‎. ‎We establish several bounds for fullerene graphs‎. ‎We also explore the automorphism group actions on the vertices and edges of these fullerene graphs‎, ‎establishing a relation between edge orbits and their eccentricities‎. ‎General formulas for calculating \textit{SDE}-indices are derived for $F_{10n}$‎, ‎when $n \geq 8$ and $F_{12n}$‎, ‎when $n \geq 10$‎. ‎Furthermore‎, ‎we present a new approach to compute the \textit{SDE}-index and then implement the method to obtain general formulas for the \textit{SDE}-index of the given classes of fullerenes‎.

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References

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Iranian Journal of Mathematical Chemistry
Volume 16, Issue 4
December 2025
Pages 355-372

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