On the number of connected subgraphs of graphs

Dinesh Pandey () and Kamal Lochan Patra ()
Additional contact information
Dinesh Pandey: National Institute of Science Education and Research (NISER)
Kamal Lochan Patra: National Institute of Science Education and Research (NISER)

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 2, 571-583

Abstract: Abstract For a connected graph G, we denote the number of connected subgraphs of G by F(G). For a tree T, F(T) has been studied extensively and it has been observed that F(T) has a reverse correlation with Wiener index of T. We call F(G), the subgraph index of G. In this paper, we study the subgraph index of unicyclic graphs and graphs with fixed number of pendant vertices. We obtain the unicyclic graphs which extremize the subgraph index over all unicyclic graphs on n vertices. The graphs which extremize the subgraph index among all unicyclic graphs with fixed girth are also obtained. Among all connected graphs on n vertices with fixed number of pendant vertices, the graph which minimizes and the graph which maximizes the subgraph index are characterized.

Keywords: Tree; Unicyclic graph; Girth; Subtree core; Wiener index; 05C05; 05C07; 05C30; 05C35 (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-021-00061-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:52:y:2021:i:2:d:10.1007_s13226-021-00061-4

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-021-00061-4

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().