On the Minimum Locating Number of Graphs with a Given Order

The chapter delves into the concept of locating sets in graphs, focusing on the minimum locating number, which is the size of the smallest set of vertices needed to uniquely identify the location of an intruder. It begins by defining locating sets and their properties, then explores the locating numbers of specific graph types such as cycles and paths. The chapter introduces propositions and lemmas to establish the minimum locating numbers for these graph structures. It also discusses the strictly locating number and provides a theorem and corollary for the minimum locating number of graphs with a given order. The chapter concludes by suggesting potential avenues for further research into the locating numbers of more complex graph structures, such as grids and hypercubes.