General eccentric connectivity index of trees and unicyclic graphs
| Autor: | Tomáš Vetrík, Mesfin Masre |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
0211 other engineering and technologies Unicyclic graphs 021107 urban & regional planning 0102 computer and information sciences 02 engineering and technology 01 natural sciences Graph Vertex (geometry) Combinatorics 010201 computation theory & mathematics Topological index Discrete Mathematics and Combinatorics Eccentric Mathematics |
| Zdroj: | Discrete Applied Mathematics. 284:301-315 |
| ISSN: | 0166-218X |
| DOI: | 10.1016/j.dam.2020.03.051 |
| Popis: | We introduce the general eccentric connectivity index of a graph G , E C I α ( G ) = ∑ v ∈ V ( G ) e c c G ( v ) d G α ( v ) for α ∈ R , where V ( G ) is the vertex set of G , e c c G ( v ) is the eccentricity of a vertex v and d G ( 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 α ≤ 1 or 0 α 1 . We present all the extremal graphs, which means that our bounds are best possible. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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