The Number of Spanning Trees for The Generalized Cones of $K_n$, The Generalized Half Cones of $K_{m,n}$ and Some Family of Modified $K_{m,n}$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912105735651328 |
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| author | Cinkir, Zubeyir |
| author_facet | Cinkir, Zubeyir |
| contents | We compute the total number of spanning trees for the generalized cone of the complete graph $K_n$ and a number of families of some modified bipartite graphs $K_{m,n}$. In particular, we obtain a new method of finding the number of spanning trees of $K_n$ and $K_{m,n}$. Our method relies on the vertex deletion formula for the number of spanning trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02874 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Number of Spanning Trees for The Generalized Cones of $K_n$, The Generalized Half Cones of $K_{m,n}$ and Some Family of Modified $K_{m,n}$ Cinkir, Zubeyir Combinatorics Primary 05C05, 05C30, 05C76 Secondary 05C38 We compute the total number of spanning trees for the generalized cone of the complete graph $K_n$ and a number of families of some modified bipartite graphs $K_{m,n}$. In particular, we obtain a new method of finding the number of spanning trees of $K_n$ and $K_{m,n}$. Our method relies on the vertex deletion formula for the number of spanning trees. |
| title | The Number of Spanning Trees for The Generalized Cones of $K_n$, The Generalized Half Cones of $K_{m,n}$ and Some Family of Modified $K_{m,n}$ |
| topic | Combinatorics Primary 05C05, 05C30, 05C76 Secondary 05C38 |
| url | https://arxiv.org/abs/2411.02874 |