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On Average Eccentricity of Graphs

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Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

The eccentricity of a vertex is the maximum distance from it to any other vertex and the average eccentricity avec(G) of a graph G is the mean value of eccentricities of all vertices of G. In this paper we present some lower and upper bounds for the average eccentricity of a connected (molecular) graph in terms of its structural parameters such as number of vertices, diameter, clique number, independence number and the first Zagreb index. Also, we obtain a relation between average eccentricity and first Zagreb index. Moreover, we compare average eccentricity with graph energy, ABC index and \(GA_1\) index.

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Acknowledgements

The second and fourth authors are partially supported by Research Project Office of Selc¸uk University. The third author is supported by Uludag university research fund, project numbers: F-2016/9, F-2015/23 and F-2015/17.

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Republic of Korea

    Kinkar Ch. Das

  2. Department of Mathematics, Faculty of Science, Selçuk University, Campus, 42075, Konya, Turkey

    A. Dilek Maden & A. Sinan Çevik

  3. Department of Mathematics, Faculty of Science and Art, Uludag University, Gorukle Campus, 16059, Bursa, Turkey

    I. Naci Cangül

Authors
  1. Kinkar Ch. Das
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  2. A. Dilek Maden
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  3. I. Naci Cangül
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  4. A. Sinan Çevik
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Correspondence to Kinkar Ch. Das.

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Das, K.C., Maden, A.D., Cangül, I.N. et al. On Average Eccentricity of Graphs. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 87, 23–30 (2017). https://doi.org/10.1007/s40010-016-0315-8

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  • DOI: https://doi.org/10.1007/s40010-016-0315-8

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