Integrating Geographic Information System and Corona Covering Number for Optimal Healthcare Placement

The allocation of medical facilities is crucial during pandemics to ensure they meet needs and are accessible during emergencies. Geographic Information Systems (GIS) play a key role in identifying areas of demand and optimizing facility placement. The corona covering set helps strategically determine facility locations to maximize coverage. Given a graph G, a set $S \subseteq V(G)$ is said to be a vertex cover set if every edge in $E(G)$ is incident with at least one vertex of S. The minimum cardinality taken over all the vertex cover sets is called the vertex covering number and it is denoted by $\alpha(G)$. A vertex cover set $S \subseteq V(G)$ is said to be a corona cover set if every vertex in $\langle S\rangle$ is either a pendant vertex or a support vertex. The minimum cardinality taken over all the corona cover sets is called the corona covering number and it is denoted as $\tau_{C}$. In this paper, we investigate strategic placement methods, utilizing Geographic Information Systems (GIS) and the corona covering set, to ensure efficient and equitable healthcare distribution during critical times, construction of Block shift graph and corona covering number