Discrete Applied Mathematics· 2026Q2
Balanced domination in convex polytopes, trees, and grid graphs
- 0citations
- Q2SCImago
- 2026year
Short summary
Three new classes of graphs (convex polytopes A_n, D_n, R_n') are proven d-balanced, and the exact balanced domination number is determined for grid graphs.
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Key points
- Three classes of convex polytopes (A_n, D_n, R_n') are shown to be d-balanced.
- A characterization of d-balancedness is provided for rooted trees with two levels of descendants.
- Full binary trees are proven to be d-balanced.
- The exact balanced domination number is determined for grid graphs.
AI-generated from the title and abstract; the full text is not read.
Abstract
This paper addresses two open questions posed in Xu et al. (2021) regarding the balanced domination number in graphs. We show that three new classes of graphs—those of convex polytopes A n , D n , and R n ′ ′ —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. Additionally, several results for caterpillar graphs are established. Moreover, we determine and prove the exact balanced domination number on grid graphs. Finally, we conclude the paper by providing several new problems of interest.
The authors' abstract, as published at the source. Discrete Applied Mathematics, 2026 · DOI ↗
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Field: Computational Theory and Mathematics
Computational Theory and MathematicsComputer Science