Balanced Domination in Convex Polytopes, Trees, and Grid Graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911258970685440 |
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| author | Nikolic, Bojan Djukanovic, Marko |
| author_facet | Nikolic, Bojan Djukanovic, Marko |
| contents | This paper addresses two open questions posed in [27] regarding the balanced domination number in graphs. We show that three new classes of graphs, those of convex polytopes A_n, D_n, and Rn'', are d-balanced. Further, we provide a characterization of d-balancedness for rooted trees with two levels of descendants and prove that each full binary tree is d-balanced. Several results for caterpillar graphs are established. Moreover, we determine and prove the exact balanced domination number for grid graphs. Finally, we conclude by providing several open problems of interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Balanced Domination in Convex Polytopes, Trees, and Grid Graphs Nikolic, Bojan Djukanovic, Marko Combinatorics 05C50, 05C69, 05C70 This paper addresses two open questions posed in [27] regarding the balanced domination number in graphs. We show that three new classes of graphs, those of convex polytopes A_n, D_n, and Rn'', are d-balanced. Further, we provide a characterization of d-balancedness for rooted trees with two levels of descendants and prove that each full binary tree is d-balanced. Several results for caterpillar graphs are established. Moreover, we determine and prove the exact balanced domination number for grid graphs. Finally, we conclude by providing several open problems of interest. |
| title | Balanced Domination in Convex Polytopes, Trees, and Grid Graphs |
| topic | Combinatorics 05C50, 05C69, 05C70 |
| url | https://arxiv.org/abs/2511.06539 |