Matching Preclusion And Conditional Matching Preclusion For Cartesian Product Of N Paths

In this thesis, we discuss about the matching preclusion and conditional match-ing preclusion of the n-grid graph which is formed by Cartesian product of n paths. This thesis is divided into three chapters. We mainly introduce the background and research status of matching preclusion and conditional matching preclusion in the first chapter. We research matching preclusion number and optimal matching preclusion set of an n-grid graph in the second chapter. If an n-grid graph has an even order, then the matching preclusion number of the n-grid graph is n and every optimal matching preclusion set of the n-grid is trivial. If an n-grid graph has an odd order, then the matching preclusion number of the n-grid graph is n+1and every optimal matching preclusion set of the n-grid graph is unique up to isomor-phism. We study conditional matching preclusion number and optimal conditional matching preclusion set of an n-grid graph in the third chapter. If an n-grid graph has an even order, then the conditional matching preclusion number of the n-grid graph is2n-1or2n-2and every optimal conditional matching preclusion set of the n-grid graph is trivial. If an n-grid graph has an odd order, then the conditional matching preclusion number of the n-grid graph is2n and every optimal conditional matching preclusion set of the n-grid graph is unique up to isomorphism.