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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 1

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

Yaser ALİZADEH
Sandi KLAVZAR
Sayfa
87–95
Yayın Tarihi
2020-02-06
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The Sz-complexity is determined for a family of (5,0)-nanotubical fullerenes and the Szeged index is compared with the total eccentricity.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Let $I$ be a summation-type topological index.
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Temel Bulgular & Veri: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 $C_{Sz}(G_m) = O_e(G_m) = m$.
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Sonuç & Katkı:The Sz-complexity is determined for a family of (5,0)-nanotubical fullerenes and the Szeged index is compared with the total eccentricity.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Szeged index · Szeged complexity · vertex-transitive graph

Abstract

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.

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Bu Makaleye Atıf Yap

ALİZADEH, Y., KLAVZAR, S. (2020). Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 87–95. https://ajindex.com/articles/669296

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