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<p>Domination of the graph and topological indices are essential topics in the graph theory. We analyze the problem of <i>k</i>-domination, <i>k</i> ∈{1, 2, 3}, on an octagonal chains and an octagonal grid. We determine the minimal <i>k</i>-dominating sets and <i>k</i>-domination numbers for a chain of octagons with two common vertices. By using the obtained results, we determine the <i>k</i>-domination numbers for the grid of octagons <i>O</i><sub><i>mxn</i></sub> with <i>m</i>, <i>n</i> ∈ <i>N</i>.</p>

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Domination Numbers on an Octagonal Chain and an Octagonal Grid

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • Miroslava Mihajlov Carević

摘要

Domination of the graph and topological indices are essential topics in the graph theory. We analyze the problem of k-domination, k ∈{1, 2, 3}, on an octagonal chains and an octagonal grid. We determine the minimal k-dominating sets and k-domination numbers for a chain of octagons with two common vertices. By using the obtained results, we determine the k-domination numbers for the grid of octagons Omxn with m, n ∈ N.