The Locating and Local Locating Domination of Prism Family Graphs

In the fields o f c ombinatorics a nd g raph t heory, prism graphs are very important.They provide insights into the structural features of many real-world networks and act as a model for them.In graph theory, the study of dominant sets is essential for a variety of applications, including social network research and network design.A dominating set in a graph G is a subset D of vertices V having the property that each vertex w belongs to V -D is neighbouring to at least one vertex D. Determining the minimum cardinal number of dominating sets, locating dominating sets, and local locating dominating sets is of critical importance in such fields as network design and social network analysis.In this paper, we determine these minimum cardinal bounds for families of prism graphs.The study adds to the basic understanding of graph theory by methodically disentangling the intricate relationships between dominating sets in prism graphs.The exploration of lowest cardinal value of locating dominating sets yields solutions to optimisation issues in network design.In this work, we determine the upper bounds of locating domination and local locating domination for prsim, antiprism, crossed prism and circulant ladder prism graph.