On the extremal eccentric connectivity index of graphs

Yueyu Wu and Yaojun Chen

Applied Mathematics and Computation, 2018, vol. 331, issue C, 61-68

Abstract: For a graph G=(V,E), the eccentric connectivity index of G, denoted by ξc(G), is defined as ξc(G)=∑v∈Vɛ(v)d(v), where ɛ(v) and d(v) are the eccentricity and the degree of v in G, respectively. In this paper, we first establish the sharp lower bound for the eccentric connectivity index in terms of the order and the minimum degree of a connected G, and characterize some extremal graphs, which generalize some known results. Secondly, we characterize the extremal trees having the maximum or minimum eccentric connectivity index for trees of order n with given degree sequence. Finally, we give a sharp lower bound for the eccentric connectivity index in terms of the order and the radius of a unicyclic G, and characterize all extremal graphs.

Keywords: Eccentric connectivity index; Minimum degree; Degree sequence; Radius (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:331:y:2018:i:c:p:61-68

DOI: 10.1016/j.amc.2018.02.042

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