General eccentric connectivity index of trees and unicyclic graphs

We introduce the general eccentric connectivity index of a graph G, ECIα(G)=∑v∈V(G)eccG(v)dGα(v) for α∈R, where V(G) is the vertex set of G, eccG(v) is the eccentricity of a vertex v and dG(v) is the degree of v in G. We present lower and upper bounds on the general eccentric connectivity index for...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2020-09, Vol.284, p.301-315
Main Authors: Vetrík, Tomáš, Masre, Mesfin
Format: Article
Language:English
Subjects:
Apexes
Connectivity
Diameter
Eccentric connectivity index
Eccentricity
Graph theory
Graphs
Pendant vertex
Tree
Trees (mathematics)
Unicyclic graph
Upper bounds
Vertex sets
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Summary:We introduce the general eccentric connectivity index of a graph G, ECIα(G)=∑v∈V(G)eccG(v)dGα(v) for α∈R, where V(G) is the vertex set of G, eccG(v) is the eccentricity of a vertex v and dG(v) is the degree of v in G. We present lower and upper bounds on the general eccentric connectivity index for trees of given order, trees of given order and diameter, and trees of given order and number of pendant vertices. Then we give lower and upper bounds on the general eccentric connectivity index for unicyclic graphs of given order, and unicyclic graphs of given order and girth. The upper bounds for trees of given order and diameter, and trees of given order and number of pendant vertices hold for α>1. All the other bounds are valid for 0
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2020.03.051