| Summary: | <p class="p1">Let <em>G</em> = (<em>V, E</em>) be a graph and <em>u,v</em> ∈ <em>V</em>. Then, <em>u</em> strongly dominates<span class="Apple-converted-space"> </span><em>v</em><span class="Apple-converted-space"> </span>if (i) <em>uv</em> ∈ <em>E</em><span class="Apple-converted-space"> </span>and (ii) deg(<em>u</em>) ≥ deg(<em>v</em>). A set <em>D</em> ⊂ <em>V</em> <span class="Apple-converted-space"> </span>is a strong-dominating set of<span class="Apple-converted-space"> </span><em>G</em><span class="Apple-converted-space"> </span>if every vertex in <em>V</em>-<em>D</em> is strongly dominated by at least one vertex in <em>D</em>. A set <em>D</em> ⊆ <em>V</em><span class="Apple-converted-space"> </span>is an independent set if no two vertices of <em>D</em><span class="Apple-converted-space"> </span>are adjacent. The independent strong domination number <em>i<sub>s</sub></em>(<em>G</em>)<span class="Apple-converted-space"> </span>of a graph <em>G</em><span class="Apple-converted-space"> </span>is the minimum cardinality of a strong dominating set which is independent. Let <em>Ġ</em> <span class="Apple-converted-space"> </span>be the complement of a graph <em>G</em>. The complementary prism <em>GĠ</em><span class="Apple-converted-space"> </span>of <em>G</em><span class="Apple-converted-space"> </span>is the graph formed from the disjoint union of <em>G</em><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span><em>Ġ</em> by adding the edges of a perfect matching between the corresponding vertices of <em>G</em><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> <em>Ġ</em></span>. In this paper, we consider the independent strong domination in complementary prisms, characterize the complementary prisms with small independent strong domination numbers, and investigate the relationship between independent strong domination number and the distance-based parameters.</p>
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