Extremal k-apex Trees for Randic Index

2015/12/07 by Naveed Akhter, Akhter, Naveed, Muhammad Kamran Jamil +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #Graph theory and applications #math.CO

paper · pdf · doi:10.48550/arxiv.1512.02127

arxiv created 2015/12/07 · arxiv updated 2015/12/08

Abstract

The Randic (connectivity) index is one of the most successful molecular descriptors in structure-property and structure-activity relationships studies. J. Gao found the sharp upper bound for the Randic index of apex trees. In this paper, we proved that k-apex trees are not regular graphs for k≥2 and proposed a sharp upper bound for the Randic index of k-apex trees for k>1.

Related

• The k-apex trees with minimum augmented Zagreb index
• On extremal trees with respect to the F-index
• The extremal generalised Randić index for a given degree range
• Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number
• First and Second Maximum of Randić Index Among all k-Cyclic Graphs of a Given Order