On the extremal eccentric connectivity index of graphs

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 th...

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Bibliographic Details
Published in:Applied mathematics and computation 2018-08, Vol.331, p.61-68
Main Authors: Wu, Yueyu, Chen, Yaojun
Format: Article
Language:English
Subjects:
Degree sequence
Eccentric connectivity index
Minimum degree
Radius
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2018.02.042