Solving sweeping problem for trees in graph theory

Abstract

We develop a theory to determine the search number of a graph that allows us to detect an intruder along an edge without limiting the visibility of adjacent vertices. The presented technique here will allow to express the sweep problem as a linear program using an existing formulation of a linear program designed for problems where capture occurs only at a vertex of a graph. We also provide a method to solve the sweep problem for any complex tree, utilizing a set of sub-trees of the tree.