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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: 1.066

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Sažetak

For a connected graph G, the eccentric connectivity index (ECI) and the first Zagreb eccentricity index of G are defined as ξc(G)=viV(G)degG(vi)εG(vi) and E1(G)=viV(G)εG(vi)2, respectively, where degG(vi) is the degree of vi in G and εG(vi) denotes the eccentricity of vertex viin G. In this paper we compare the eccentric connectivity index and the first Zagreb eccentricity index of graphs. It is proved that E1(T)>ξc(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 E1(G)>ξc(G). We also present an example in which infinite graphs G are constructed with E1(G)=ξc(G) and give some results on the graphs G with E1(G)<ξc(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

URI

https://hrcak.srce.hr/181033

Datum izdavanja:

19.12.2016.

Posjeta: 1.948 *

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