| Autor: |
Sarmin, Nor Haniza, Mudaber, Mohammad Hassan, Gambo, Ibrahim |
| Předmět: |
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| Zdroj: |
AIP Conference Proceedings; 2024, Vol. 3189 Issue 1, p1-6, 6p |
| Abstrakt: |
A graph formed by deleting the non-units of a commutative ring R from the complement unit graph, where the units of R represent its vertex set, is referred to as an induced subgraph. A subset C of the vertex set of an induced subgraph of a complement unit graph of R is called a perfect code if the balls of radius 1 centered at C form a partition of the vertex set. In this paper, our focus is on investigating perfect codes within induced subgraphs of complement unit graphs associated with specific commutative rings containing unity. Therefore, by establishing some mathematical theorems, we characterize R for which the induced subgraphs of the complement unit graphs admit either a trivial or a non-trivial perfect code. In addition, some examples are provided as applications of the theorems. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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