Graph Cordiality -- Extremes and Preservers
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913480236335104 |
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| author | Beasley, LeRoy b. |
| author_facet | Beasley, LeRoy b. |
| contents | An undirected graph is said to be cordial if there is a friendly (0,1)-labeling of the vertices that induces a friendly (0,1)-labeling of the edges. An undirected graph $G$ is said to be $(2,3)$-orientable if there exists a friendly (0,1)-labeling of the vertices of $G$ such that about one third of the edges are incident to vertices labeled the same. That is, there is some digraph that is an orientation of $G$ that is $(2,3)$-cordial. Examples of the smallest noncordial/non-$(2,3)$-orientable graphs are given and upper bounds on the possible number of edges in a cordial/$(2,3)$-orientable graph are presented. It is also shown that if $T$ is a linear operator on the set of all undirected graphs on $n$ vertices that strongly preserves the set of cordial graphs or the set of $(2,3)$-orientable graphs then $T$ is a vertex permutation.. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13853 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graph Cordiality -- Extremes and Preservers Beasley, LeRoy b. Combinatorics 05C20, 05C60, 05C78 An undirected graph is said to be cordial if there is a friendly (0,1)-labeling of the vertices that induces a friendly (0,1)-labeling of the edges. An undirected graph $G$ is said to be $(2,3)$-orientable if there exists a friendly (0,1)-labeling of the vertices of $G$ such that about one third of the edges are incident to vertices labeled the same. That is, there is some digraph that is an orientation of $G$ that is $(2,3)$-cordial. Examples of the smallest noncordial/non-$(2,3)$-orientable graphs are given and upper bounds on the possible number of edges in a cordial/$(2,3)$-orientable graph are presented. It is also shown that if $T$ is a linear operator on the set of all undirected graphs on $n$ vertices that strongly preserves the set of cordial graphs or the set of $(2,3)$-orientable graphs then $T$ is a vertex permutation.. |
| title | Graph Cordiality -- Extremes and Preservers |
| topic | Combinatorics 05C20, 05C60, 05C78 |
| url | https://arxiv.org/abs/2408.13853 |