Domination polynomial of co-maximal graphs of integer modulo ring
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910047115673600 |
|---|---|
| author | Rather, Bilal Ahmad |
| author_facet | Rather, Bilal Ahmad |
| contents | We investigate the domination polynomial of the co-maximal graph $Γ(\mathbb{Z}_n)$ related to the ring of integers modulo $n$. Explicit formulas are derived for \( n = p^{n_1} \) and \( n = p^{n_1}q^{n_2} \), demonstrating that the resulting polynomials exhibit unimodality and log-concavity. For general $n$, we present structural expressions that connect $D(Γ(\mathbb{Z}_n),x)$ to appropriate induced subgraphs. Finally, we examine domination roots and establish bounds for their moduli using the Eneström--Kakeya theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08867 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Domination polynomial of co-maximal graphs of integer modulo ring Rather, Bilal Ahmad Combinatorics Discrete Mathematics 05C25, 05C31, 11S05, 12D10 F.2.2 We investigate the domination polynomial of the co-maximal graph $Γ(\mathbb{Z}_n)$ related to the ring of integers modulo $n$. Explicit formulas are derived for \( n = p^{n_1} \) and \( n = p^{n_1}q^{n_2} \), demonstrating that the resulting polynomials exhibit unimodality and log-concavity. For general $n$, we present structural expressions that connect $D(Γ(\mathbb{Z}_n),x)$ to appropriate induced subgraphs. Finally, we examine domination roots and establish bounds for their moduli using the Eneström--Kakeya theorem. |
| title | Domination polynomial of co-maximal graphs of integer modulo ring |
| topic | Combinatorics Discrete Mathematics 05C25, 05C31, 11S05, 12D10 F.2.2 |
| url | https://arxiv.org/abs/2603.08867 |