| Summary: | <p>A subset <em>S</em> of vertices in graph <em>G</em> is called a <em>geodetic set</em> if every vertex in <em>V</em>(<em>G</em>) \ <em>S</em> lies on a shortest path between two vertices in <em>S</em>. A subset <em>S</em> of vertices in <em>G</em> is called a <em>dominating set</em> if every vertex in <em>V</em>(<em>G</em>) \ <em>S</em> is adjacent to a vertex in <em>S</em>. The set <em>S</em> is called a <em>geodetic dominating set</em> if <em>S</em> is both geodetic and dominating sets. The <em>geodetic domination number</em> of <em>G</em>, denoted by <em>γ<sub>g</sub></em>(<em>G</em>), is the minimum cardinality of geodetic domination sets in <em>G</em>. The <em>comb product</em> of connected graphs <em>G</em> and <em>H</em> at vertex o ∈ <em>V</em>(<em>H</em>), denoted by <em>G ∇<sub>o</sub> H</em>, is a graph obtained by taking one copy of <em>G</em> and |<em>V</em>(<em>G</em>)| copies of <em>H</em> and identifying the <em>i</em><sup>th</sup> copy of <em>H</em> at the vertex <em>o</em> to the <em>i</em><sup>th</sup> vertex of <em>G</em>. In this paper, we determine an exact value of <em>γ<sub>g</sub></em>(<em>G ∇<sub>o</sub> H</em>) for any connected graphs <em>G</em> and <em>H</em>.</p>
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