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## Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes

#### Yaser ALİZADEH [1] , Sandi KLAVZAR [2]

Let $I$ be a summation-type topological index. The $I$-complexity $C_I(G)$ of a graph $G$ is the number of different contributions to $I(G)$ in its summation formula. In this paper the complexity $C_{Sz}(G)$ is investigated, where Sz is the well-studied Szeged index. Let $O_e(G)$ (resp. $O_v(G)$) be the number of edge (resp. vertex) orbits of $G$. While $C_{Sz}(G) \leq O_e(G)$ holds for any graph $G$, it is shown that for any $m\geq 1$ there exists a vertex-transitive graph $G_m$ with $C_{Sz}(G_m) = O_e(G_m) = m$. Also, for any $1\leq k\leq m+1$ there exists a graph $G_{m,k}$ with $C_{Sz}(G_{m,k}) = O_e(G_{m,k}) = m$ and $C_{W}(G_{m,k}) = O_v(G_{m,k}) = k$. The Sz-complexity is determined for a family of (5,0)-nanotubical fullerenes and the Szeged index is compared with the total eccentricity.
Szeged index, Szeged complexity, vertex-transitive graph, edge-transitive graphs, fullerene, total eccentricity
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-8533-0425Author: Yaser ALİZADEH Institution: Hakim Sabzevari UniversityCountry: Iran Orcid: 0000-0002-1556-4744Author: Sandi KLAVZAR (Primary Author)Institution: University of LjubljanaCountry: Slovenia Publication Date : February 6, 2020
 Bibtex @research article { hujms534992, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {87 - 95}, doi = {10.15672/HJMS.2019.664}, title = {Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes}, key = {cite}, author = {ALİZADEH, Yaser and KLAVZAR, Sandi} } APA ALİZADEH, Y , KLAVZAR, S . (2020). Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 87-95 . DOI: 10.15672/HJMS.2019.664 MLA ALİZADEH, Y , KLAVZAR, S . "Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 87-95 Chicago ALİZADEH, Y , KLAVZAR, S . "Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 87-95 RIS TY - JOUR T1 - Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes AU - Yaser ALİZADEH , Sandi KLAVZAR Y1 - 2020 PY - 2020 N1 - doi: 10.15672/HJMS.2019.664 DO - 10.15672/HJMS.2019.664 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 87 EP - 95 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2019.664 UR - https://doi.org/10.15672/HJMS.2019.664 Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes %A Yaser ALİZADEH , Sandi KLAVZAR %T Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/HJMS.2019.664 %U 10.15672/HJMS.2019.664 ISNAD ALİZADEH, Yaser , KLAVZAR, Sandi . "Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 87-95 . https://doi.org/10.15672/HJMS.2019.664 AMA ALİZADEH Y , KLAVZAR S . Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 87-95. Vancouver ALİZADEH Y , KLAVZAR S . Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 95-87.

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