Bicyclic graphs with the smallest and largest numbers of connected sets
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911548878880768 |
|---|---|
| author | Dossou-Olory, Audace A. V. |
| author_facet | Dossou-Olory, Audace A. V. |
| contents | For a graph $G$ with vertex set $V$, let N($G$) denote the number of nonempty subsets of $V$ that induce a connected graph in $G$. In this paper, we focus on determining N($G$) for $G$ in the family $\mathbb{B}_n$ of $n$-vertex bicyclic graphs. We find in $\mathbb{B}_n$ the structures of those graphs that possess the smallest, the largest, as well as the second-largest values of N($G$). Moreover, we compute the extreme values of N($G$) over $\mathbb{B}_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26812 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bicyclic graphs with the smallest and largest numbers of connected sets Dossou-Olory, Audace A. V. Combinatorics Primary 05C30, secondary 05C35, 05C69, 05C75 For a graph $G$ with vertex set $V$, let N($G$) denote the number of nonempty subsets of $V$ that induce a connected graph in $G$. In this paper, we focus on determining N($G$) for $G$ in the family $\mathbb{B}_n$ of $n$-vertex bicyclic graphs. We find in $\mathbb{B}_n$ the structures of those graphs that possess the smallest, the largest, as well as the second-largest values of N($G$). Moreover, we compute the extreme values of N($G$) over $\mathbb{B}_n$. |
| title | Bicyclic graphs with the smallest and largest numbers of connected sets |
| topic | Combinatorics Primary 05C30, secondary 05C35, 05C69, 05C75 |
| url | https://arxiv.org/abs/2603.26812 |