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On Connected Graphs Having the Maximum Connective Eccentricity Index

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Abstract

The connective eccentricity index (CEI) of a connected graph G is defined as \(\xi ^{ee}(G)=\sum _{u\in V_G}[d_G(u)/\varepsilon _G(u)]\), where \(d_G(u)\) and \(\varepsilon _G(u)\) are the degree and eccentricity, respectively, of the vertex \(u\in V_G\) of G. In this paper, graphs with the maximum CEI are characterized from the class of all connected graphs of a fixed order and size. Graphs having maximum CEI are also determined from some other well-known classes of connected graphs of a given order; namely, the Halin graphs, triangle-free graphs, planar graphs and outer-planar graphs.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Central China Normal University, Wuha, 430079, People’s Republic of China

    Shahid Zaman

  2. Department of Mathematics, University of Sialkot, Sialkot, 51310, Pakistan

    Shahid Zaman

  3. Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il, Saudi Arabia

    Akbar Ali

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  1. Shahid Zaman
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Zaman, S., Ali, A. On Connected Graphs Having the Maximum Connective Eccentricity Index. J. Appl. Math. Comput. 67, 131–142 (2021). https://doi.org/10.1007/s12190-020-01489-3

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  • DOI: https://doi.org/10.1007/s12190-020-01489-3

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