An edge labeling of graphs from Rados partition regularity condition
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910831887777792 |
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| author | Manattu, Arun J S, Aparna Lakshmanan |
| author_facet | Manattu, Arun J S, Aparna Lakshmanan |
| contents | A vertex $v$ is called an AR-vertex, if $v$ has distinct edge weight sums for each distinct subset of edges incident on $v$. i.e., if $\{x_1,x_2,\dots,x_k\}$ are the edge labels of the edges incident on $v$, then the $2^k$ subset sums are all distinct. An injective edge labeling $f$ of a graph $G$ is said to be an AR-labeling of $G$, if $f:E \rightarrow \mathbb{N}$ is such that every vertex in $G$ is an AR-vertex under $f$. A graph $G$ is said to be an AR-graph, if there exists an AR-labeling $f:E\rightarrow \{1,2,\dots,m\}$, where $m$ denotes the number of edges of $G$. A study of AR-labeling and AR-graphs is initiated in this paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_11760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An edge labeling of graphs from Rados partition regularity condition Manattu, Arun J S, Aparna Lakshmanan Combinatorics 05C78, 05C55 A vertex $v$ is called an AR-vertex, if $v$ has distinct edge weight sums for each distinct subset of edges incident on $v$. i.e., if $\{x_1,x_2,\dots,x_k\}$ are the edge labels of the edges incident on $v$, then the $2^k$ subset sums are all distinct. An injective edge labeling $f$ of a graph $G$ is said to be an AR-labeling of $G$, if $f:E \rightarrow \mathbb{N}$ is such that every vertex in $G$ is an AR-vertex under $f$. A graph $G$ is said to be an AR-graph, if there exists an AR-labeling $f:E\rightarrow \{1,2,\dots,m\}$, where $m$ denotes the number of edges of $G$. A study of AR-labeling and AR-graphs is initiated in this paper. |
| title | An edge labeling of graphs from Rados partition regularity condition |
| topic | Combinatorics 05C78, 05C55 |
| url | https://arxiv.org/abs/2502.11760 |