Report
New Optimal Results on Codes for Location in Graphs
| العنوان: | New Optimal Results on Codes for Location in Graphs |
|---|---|
| المؤلفون: | Junnila, Ville, Laihonen, Tero, Lehtilä, Tuomo |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Discrete Mathematics, Mathematics - Combinatorics, 05C69, 05C76, 05C63, G.2.2 |
| الوصف: | In this paper, we broaden the understanding of the recently introduced concepts of solid-locating-dominating and self-locating-dominating codes in various graphs. In particular, we present the optimal, i.e., smallest possible, codes in the infinite triangular and king grids. Furthermore, we give optimal locating-dominating, self-locating-dominating and solid-locating-dominating codes in the direct product $K_n\times K_m$ of complete graphs. We also present optimal solid-locating-dominating codes for the Hamming graphs $K_q\square K_q\square K_q$ with $q\geq2$. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2306.07862 |
| رقم الانضمام: | edsarx.2306.07862 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |