Strategic Defense Post Allocation Using the Corona Cover Set for Enhanced Military Zone Security

Defense forces are vital for national safety, peace-keeping, disaster response, and economic support. They require strong support systems, medical access, rapid deployment, and effective command centers to operate efficiently. Proper placement and a well-structured defense strategy focusing on sustainability and readiness are essential for ensuring safety and stability for both military and civilians. Recently G. Mahadevan et.al established the concept of Corona covering number of a graph and obtained many results. A vertex cover set <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$S\subseteq V(G)$</tex> is a corona cover set if every vertex <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$v\in S$</tex> such that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d_{\langle S\rangle}(v)=1$</tex> or there exist a vertex <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$u\in S$</tex> with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d_{\langle S\rangle}(u)=1$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$uv\in E$</tex>. The least cardinality of a corona cover set is the corona covering number of a graph and it is expressed as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tau_{C}(G)$</tex>. In this article, the investigation of corona covering number in the strategic placement of defense posts within military zones, aiming to enhance operational efficiency and effectively deter unauthorized incursions has been attained.