On vertex peripherians and Wiener index of graphs with fixed number of cut vertices
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916323201646592 |
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| author | Pandey, Dinesh |
| author_facet | Pandey, Dinesh |
| contents | The distance of a vertex in a graph is the sum of distances from that vertex to all other vertices of the graph. The Wiener index of a graph is the sum of distances between all its unordered pairs of vertices. A graph has been obtained that contains a vertex achieving the maximum distance among all graphs on $n$ vertices with fixed number of cut vertices. Further the graphs having maximum Wiener index among all graphs on $n$ vertices with at most $3$ cut vertices have been characterised. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10288 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On vertex peripherians and Wiener index of graphs with fixed number of cut vertices Pandey, Dinesh Combinatorics 05C09, 05C12, 05C35 The distance of a vertex in a graph is the sum of distances from that vertex to all other vertices of the graph. The Wiener index of a graph is the sum of distances between all its unordered pairs of vertices. A graph has been obtained that contains a vertex achieving the maximum distance among all graphs on $n$ vertices with fixed number of cut vertices. Further the graphs having maximum Wiener index among all graphs on $n$ vertices with at most $3$ cut vertices have been characterised. |
| title | On vertex peripherians and Wiener index of graphs with fixed number of cut vertices |
| topic | Combinatorics 05C09, 05C12, 05C35 |
| url | https://arxiv.org/abs/2407.10288 |