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On the ABC index of connected graphs with given degree sequences.
- Source :
-
Journal of Mathematical Chemistry . Feb2018, Vol. 56 Issue 2, p568-582. 15p. - Publication Year :
- 2018
-
Abstract
- The atom-bond connectivity (ABC) index of a graph G is defined to be $$ABC(G)=\sum _{uv\in E(G)}\sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}}$$ where d( u) is the degree of a vertex u. The ABC index plays a key role in correlating the physical-chemical properties and the molecular structures of some families of compounds. In this paper, we describe the structural properties of graphs which have the minimum ABC index among all connected graphs with a given degree sequence. Moreover, these results are used to characterize the extremal graphs which have the minimum ABC index among all unicyclic and bicyclic graphs with a given degree sequence. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02599791
- Volume :
- 56
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Chemistry
- Publication Type :
- Academic Journal
- Accession number :
- 127331141
- Full Text :
- https://doi.org/10.1007/s10910-017-0802-4