On the eccentric graph of trees
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914890035232768 |
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| author | Sorgun, Sezer Elyemani, Esma |
| author_facet | Sorgun, Sezer Elyemani, Esma |
| contents | We consider the eccentric graph of a graph $G$, denoted by $ecc(G)$, which has the same vertex set as $G$, and two vertices in the eccentric graph are adjacent iff their distance in $G$ is equal to the eccentricity of one of them. In this paper, we present a fundamental requirement for the isomorphism between $ecc(G)$ and the complement of $G$, and show that the previous necessary condition given in the literature is inadequate. Also we obtain that diameter of $ecc(T)$ is at most $3$ for any tree and get some characterizations of the eccentric graph of trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03835 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the eccentric graph of trees Sorgun, Sezer Elyemani, Esma Combinatorics 05C50 We consider the eccentric graph of a graph $G$, denoted by $ecc(G)$, which has the same vertex set as $G$, and two vertices in the eccentric graph are adjacent iff their distance in $G$ is equal to the eccentricity of one of them. In this paper, we present a fundamental requirement for the isomorphism between $ecc(G)$ and the complement of $G$, and show that the previous necessary condition given in the literature is inadequate. Also we obtain that diameter of $ecc(T)$ is at most $3$ for any tree and get some characterizations of the eccentric graph of trees. |
| title | On the eccentric graph of trees |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2307.03835 |