| Summary: | Location detection is studied for many scenarios, such as pointing out the flaws in multiprocessors, invaders in buildings and facilities, and utilizing wireless sensor networks for monitoring environmental processes. The system or structure can be illustrated as a graph in each of these applications. Sensors strategically placed at a subset of vertices can determine and identify irregularities within the network. The open locating-dominating set <i>S</i> of a graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></semantics></math></inline-formula> is the set of vertices that dominates <i>G</i>, and for any <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>,</mo><mi>j</mi><mo>∈</mo></mrow></semantics></math></inline-formula> V(G) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>(</mo><mi>i</mi><mo>)</mo><mo>∩</mo><mi>S</mi><mo>≠</mo><mi>N</mi><mo>(</mo><mi>j</mi><mo>)</mo><mo>∩</mo><mi>S</mi></mrow></semantics></math></inline-formula> is satisfied. The set <i>S</i> is called the OLD-set of <i>G</i>. The cardinality of the set <i>S</i> is called open locating-dominating number and denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>γ</mi><mrow><mi>o</mi><mi>l</mi><mi>d</mi></mrow></msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. In this paper, we computed exact values of the prism and prism-related graphs, and also the exact values of convex polytopes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mi>n</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mi>n</mi></msub></semantics></math></inline-formula>. The upper bound is determined for other classes of convex polytopes. The graphs considered here are well-known from the literature.
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