On the number of connected edge cover sets in a graph
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912163179790336 |
|---|---|
| author | Zare, Mahsa Alikhani, Saeid Oboudi, Mohammad Reza |
| author_facet | Zare, Mahsa Alikhani, Saeid Oboudi, Mohammad Reza |
| contents | Let $ G=(V,E) $ be a simple graph of order $ n $ and size $ m $. A connected edge cover set of a graph is a subset $S$ of edges such that every vertex of the graph is incident to at least one edge of $S$ and the subgraph induced by $S$ is connected. We initiate the study of the number of the connected edge cover sets of a graph $G$ with cardinality $i$, $ e_{c}(G,i) $ and consider the generating function for $ e_{c}(G,i) $ which is called the connected edge cover polynomial of $ G $. After obtaining some results for this polynomial, we investigate this polynomial for some certain graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15688 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the number of connected edge cover sets in a graph Zare, Mahsa Alikhani, Saeid Oboudi, Mohammad Reza Combinatorics 05C30, 05C69 Let $ G=(V,E) $ be a simple graph of order $ n $ and size $ m $. A connected edge cover set of a graph is a subset $S$ of edges such that every vertex of the graph is incident to at least one edge of $S$ and the subgraph induced by $S$ is connected. We initiate the study of the number of the connected edge cover sets of a graph $G$ with cardinality $i$, $ e_{c}(G,i) $ and consider the generating function for $ e_{c}(G,i) $ which is called the connected edge cover polynomial of $ G $. After obtaining some results for this polynomial, we investigate this polynomial for some certain graphs. |
| title | On the number of connected edge cover sets in a graph |
| topic | Combinatorics 05C30, 05C69 |
| url | https://arxiv.org/abs/2412.15688 |