Croatica Chemica Acta,Vol. 89 No. 4, 2016.

Kratko priopćenje
https://doi.org/10.5562/cca3028

Comparison Between Two Eccentricity-based Topological Indices of Graphs

Kexiang Xu ; College of Science, Nanjing University of Aeronautics & Astronautics, Nanjing, Jiangsu 210016, PR China
Xia Li ; College of Science, Nanjing University of Aeronautics & Astronautics, Nanjing, Jiangsu 210016, PR China

 Puni tekst: engleski, pdf (625 KB) str. 499-504 preuzimanja: 623* citiraj APA 6th EditionXu, K. i Li, X. (2016). Comparison Between Two Eccentricity-based Topological Indices of Graphs. Croatica Chemica Acta, 89 (4), 499-504. https://doi.org/10.5562/cca3028 MLA 8th EditionXu, Kexiang i Xia Li. "Comparison Between Two Eccentricity-based Topological Indices of Graphs." Croatica Chemica Acta, vol. 89, br. 4, 2016, str. 499-504. https://doi.org/10.5562/cca3028. Citirano 20.10.2021. Chicago 17th EditionXu, Kexiang i Xia Li. "Comparison Between Two Eccentricity-based Topological Indices of Graphs." Croatica Chemica Acta 89, br. 4 (2016): 499-504. https://doi.org/10.5562/cca3028 HarvardXu, K., i Li, X. (2016). 'Comparison Between Two Eccentricity-based Topological Indices of Graphs', Croatica Chemica Acta, 89(4), str. 499-504. https://doi.org/10.5562/cca3028 VancouverXu K, Li X. Comparison Between Two Eccentricity-based Topological Indices of Graphs. Croatica Chemica Acta [Internet]. 2016 [pristupljeno 20.10.2021.];89(4):499-504. https://doi.org/10.5562/cca3028 IEEEK. Xu i X. Li, "Comparison Between Two Eccentricity-based Topological Indices of Graphs", Croatica Chemica Acta, vol.89, br. 4, str. 499-504, 2016. [Online]. https://doi.org/10.5562/cca3028

Sažetak
For a connected graph $G$, the eccentric connectivity index (ECI) and the first Zagreb eccentricity index of $G$ are defined as $\xi ^{c}(G)= \sum_{v_i \in V(G)}\deg_G(v_i)\varepsilon_G(v_i)$ and $E_1(G)=\sum_{v_i\in V(G)}\varepsilon_{G}(v_i)^{2}$, respectively, where $\deg_G(v_i)$ is the degree of $v_i$ in $G$ and $\varepsilon_G(v_i)$ denotes the eccentricity of vertex $v_i$in $G$. In this paper we compare the eccentric connectivity index and the first Zagreb eccentricity index of graphs. It is proved that $E_1(T)>\xi^c(T)$ for any tree $T$. This improves a result by Das[25] for the chemical trees. Moreover, we also show that there are infinite number of chemical graphs $G$ with $E_1(G)>\xi^c(G)$. We also present an example in which infinite graphs $G$ are constructed with $E_1(G)=\xi^c(G)$ and give some results on the graphs $G$ with $E_1(G)<\xi^c(G)$. Finally, an effective construction is proposed for generating infinite graphs with each comparative inequality possibility between these two topological indices.

Ključne riječi
Graph; First Zagreb eccentricity index; Eccentric connectivity index

Hrčak ID: 181033

Posjeta: 891 *