The Symmetric Division Eccentric Index of Two Infinite Classes of Fullerenes
نویسندگان
1 Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-163, I. R. Iran
2 Department of Mathematics, Salahaddin University-Erbil, Kurdistan, Iraq
3 Department of Mathematics, Salahaddin University-Erbil, Kurdistan, Iraq
doi
10.22052/ijmc.2025.255411.1998چکیده
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.
