Marcello's completion of graphs
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909674231562240 |
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| author | Kok, Johan |
| author_facet | Kok, Johan |
| contents | This paper initiates a study on a new optimization problem with regards to graph completion. The defined procedure is called, \emph{Marcello's completion} of a graph. For graph $G$ of order $n$ the \emph{Marcello number} is obtained by iteratively constructing graphs, $G_1,G_2,\dots,G_k$ by adding a maximal number of edges between pairs of distinct, non-adjacent vertices in accordance with the \emph{Marcello rule}. If for smallest $k$ the resultant graph $G_k \cong K_n$ then the Marcello number of a graph $G$ denoted by $\varpi(G)$ is equal to $\varpi(G) = k$. By convention $\varpi(K_n) = 0$, $n \geq 1$. Certain introductory results are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02015 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Marcello's completion of graphs Kok, Johan Combinatorics 05C07, 05C09, 05C30, 05C69, 05C82 This paper initiates a study on a new optimization problem with regards to graph completion. The defined procedure is called, \emph{Marcello's completion} of a graph. For graph $G$ of order $n$ the \emph{Marcello number} is obtained by iteratively constructing graphs, $G_1,G_2,\dots,G_k$ by adding a maximal number of edges between pairs of distinct, non-adjacent vertices in accordance with the \emph{Marcello rule}. If for smallest $k$ the resultant graph $G_k \cong K_n$ then the Marcello number of a graph $G$ denoted by $\varpi(G)$ is equal to $\varpi(G) = k$. By convention $\varpi(K_n) = 0$, $n \geq 1$. Certain introductory results are presented. |
| title | Marcello's completion of graphs |
| topic | Combinatorics 05C07, 05C09, 05C30, 05C69, 05C82 |
| url | https://arxiv.org/abs/2507.02015 |