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.

中文翻译：

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具有最大连接偏心率索引的连通图

连接图G的连接偏心率指数（CEI）定义为\（\ xi ^ {ee}（G）= \ sum _ {u \ in V_G} [d_G（u）/ \ varepsilon _G（u）] \ ），其中\（d_G（u）\）和\（\ varepsilon _G（u）\）分别是G顶点\（u_in V_G \）的度数和偏心率。在本文中，具有最大CEI的图是通过固定顺序和大小的所有连接图的类别来表征的。具有最大CEI的图也从给定顺序的一些其他知名类的连接图中确定；即Halin图，无三角形图，平面图和外平面图。