Work

Balanced domination in convex polytopes, trees, and grid graphs

Year: 2026

Type: article

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.

Source: Discrete Applied Mathematics

DOI: 10.1016/j.dam.2026.09.021

Authors: Bojan Nikolic, Marko Djukanovic

Institutions: University of Banja Luka, University of Nova Gorica, Institute of Information Science

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090