Abstract
For a connected simple graph G, the eccentricity ec(v) of a vertex v in G is the distance from v to a vertex farthest from v, and d(v) denotes the degree of a vertex v. The eccentric connectivity index of G, denoted by ξ c(G), is defined as Σ v∈V(G) d(v)ec(v). In this paper, we will determine the graphs with maximal eccentric connectivity index among the connected graphs with n vertices and m edges(n ≤ m ≤ n+4), and propose a conjecture on the graphs with maximal eccentric connectivity index among the connected graphs with n vertices and m edges (m ≥ n +5).
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Supported by China Postdoctoral Science Foundation (2012M520815 and 2013T60411), and the National Natural Science Foundation of China (11001089).
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Zhang, Jb., Liu, Zz. & Zhou, B. On the maximal eccentric connectivity indices of graphs. Appl. Math. J. Chin. Univ. 29, 374–378 (2014). https://doi.org/10.1007/s11766-014-3023-7
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DOI: https://doi.org/10.1007/s11766-014-3023-7