Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.08853 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918123806916608 |
|---|---|
| author | Sharma, Arati Guragain, Satyam Srivastava, Ravi |
| author_facet | Sharma, Arati Guragain, Satyam Srivastava, Ravi |
| contents | Connectivity is one of the central ideas in graph theory, especially when it comes to building fault-tolerant networks. A cutset $S$ of $G$ is defined to be the set of vertices in $G$ whose removal disconnects the graph. An $R_g$ cutset of $G$ is a cutset whose removal disconnects the graph in such a way that each connected component has at least $g+1$ vertices. If $G$ has at least one $R_g$ cutset then the $g-$extra vertex connectivity (or the $g-$extra edge connectivity), denoted as $κ_g(G)$ ($λ_g(G)$), is defined as the minimum cardinality of $R_g$ cutset. In this paper, we obtain the $g-$ extra connectivity of various corona type graph products edge corona, neighbourhood corona, subdivision vertex neighbourhood corona,subdivision edge neighbourhood corona and generalised corona product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On g-Extra Connectivity of Corona-Type Graph Products Sharma, Arati Guragain, Satyam Srivastava, Ravi Combinatorics 05C40 Connectivity is one of the central ideas in graph theory, especially when it comes to building fault-tolerant networks. A cutset $S$ of $G$ is defined to be the set of vertices in $G$ whose removal disconnects the graph. An $R_g$ cutset of $G$ is a cutset whose removal disconnects the graph in such a way that each connected component has at least $g+1$ vertices. If $G$ has at least one $R_g$ cutset then the $g-$extra vertex connectivity (or the $g-$extra edge connectivity), denoted as $κ_g(G)$ ($λ_g(G)$), is defined as the minimum cardinality of $R_g$ cutset. In this paper, we obtain the $g-$ extra connectivity of various corona type graph products edge corona, neighbourhood corona, subdivision vertex neighbourhood corona,subdivision edge neighbourhood corona and generalised corona product. |
| title | On g-Extra Connectivity of Corona-Type Graph Products |
| topic | Combinatorics 05C40 |
| url | https://arxiv.org/abs/2508.08853 |