On the existence of neutral graph
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915754762305536 |
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| author | Ma, Fei |
| author_facet | Ma, Fei |
| contents | Graph is considered neutral if its assortativity coefficient $r$ is equal to zero. In this paper, we address an outstanding conjecture, i.e., whether is there a neutral graph on $n$ vertices? First, we show that for $n\geq7$, there is at least one neutral tree, which suggests that we find a representative of any order neutral graph. Additionally, we obtain that given $n\geq13$, there exists at least one neutral non-tree graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the existence of neutral graph Ma, Fei Combinatorics 05C09, 05C76 Graph is considered neutral if its assortativity coefficient $r$ is equal to zero. In this paper, we address an outstanding conjecture, i.e., whether is there a neutral graph on $n$ vertices? First, we show that for $n\geq7$, there is at least one neutral tree, which suggests that we find a representative of any order neutral graph. Additionally, we obtain that given $n\geq13$, there exists at least one neutral non-tree graph. |
| title | On the existence of neutral graph |
| topic | Combinatorics 05C09, 05C76 |
| url | https://arxiv.org/abs/2511.21426 |