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Cacti with extremal PI Index

Authors :
Chunxiang Wang
Shaohui Wang
Bing Wei
Source :
Transactions on Combinatorics, Vol 5, Iss 4, Pp 1-8 (2016)
Publication Year :
2016
Publisher :
University of Isfahan, 2016.

Abstract

The vertex PI index $PI(G) = sum_{xy in E(G)} [n_{xy}(x)‎ + ‎n_{xy}(y)]$ is a distance-based molecular structure descriptor‎, ‎where $n_{xy}(x)$ denotes the number of vertices which are closer to the vertex $x$ than to the vertex $y$ and which has been the considerable research in computational chemistry dating back to Harold Wiener in 1947‎. ‎A connected graph is a cactus if any two of its cycles have at most one common vertex‎. ‎In this paper‎, ‎we completely determine the extremal graphs with the greatest and smallest vertex PI indices mong all cacti with a fixed number of vertices‎. ‎As a consequence‎, ‎we obtain the sharp bounds with corresponding extremal cacti and extend a known result‎.

Details

Language :
English
ISSN :
22518657 and 22518665
Volume :
5
Issue :
4
Database :
Directory of Open Access Journals
Journal :
Transactions on Combinatorics
Publication Type :
Academic Journal
Accession number :
edsdoj.11c0b88c330446e3abcd14000fc44fc9
Document Type :
article
Full Text :
https://doi.org/10.22108/toc.2016.14786