ScholarLens Back to search
2011•Unpublished venueRequires access

Extreme Atom-Bond Connectivity Index of Graphs

J. S. Chen, X. F. Guo, 郭晓峰

Open publisher page 66 citations

Abstract

The atom-bond connectivity (ABC) index of a graph G, is defined as the sum of the weights (du + dv − 2 dudv ) 1 2 of all edges uv of G, where du denotes the degree of a vertex u in G. The ABC index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes. In this paper, we characterize the catacondensed hexagonal systems with extreme ABC indices, and prove that the ABC index of a graph decreases when any edge is deleted. Consequently, it is also proved that the graph with n vertices and the maximum ABC index is the complete graph Kn.

About this research paper

What this paper is about

The atom-bond connectivity (ABC) index of a graph G, is defined as the sum of the weights (du + dv − 2 dudv ) 1 2 of all edges uv of G, where du denotes the degree of a vertex u in G. The ABC index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes. In this paper, we characterize the catacondensed hexagonal systems with extreme ABC indices, and prove that the ABC index of a graph decreases when any edge is deleted. Consequently, it is also proved that the graph with n vertices and the maximum ABC index is the complete graph Kn.

Why it matters

OpenAlex reports 66 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

The atom-bond connectivity (ABC) index of a graph G, is defined as the sum of the weights (du + dv − 2 dudv ) 1 2 of all edges uv of G, where du denotes the degree of a vertex u in G. The ABC index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes. In this paper, we characterize the catacondensed hexagonal systems with extreme ABC indices, and prove that the ABC index of a graph decreases when any edge is deleted. Consequently, it is also proved that the graph with n vertices and the maximum ABC index is the complete graph Kn.

Key concepts: Combinatorics, Topological index, Vertex (graph theory), Mathematics, Graph, Discrete mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Extreme Atom-Bond Connectivity Index of Graphs — Research Paper | ScholarLens