Research On Special Matchings Of Several Types Of Graphs

A matching of graph G is edges and no two edges are adjacent.A matching in graph G is uniquely restricted if no other matching in G covers exactly the same set of vertices.A matching in graph G is acyclic if the subgraph of G induced by the set of vertices of G covered by M is a forest.This paper mainly studies the maximum uniquely restricted matching number,acyclic matching number and the number of perfect matching for Cartesian product of graphs.In the first and the second chapter,the research background and research status at home and abroad are mainly introduced.In the third chapter and the forth chapter,we obtain the maximum number of the uniquely restricted matching and the acyclic matching of the product graphs Pk×P2,Pk×P3,Pk×S1,m.The maximum uniquely restricted matching number and the maximum acyclic matching number of the graph classes Gk,Lk are obtained by adding edges to the product graph Pk×P2.In the fifth chapter,the equivalence conditions of the uniquely restricted matching and the acyclic matching in the unicycle bipartite graph are described.In the sixth chapter,we get the uniquely restricted matching counts and acyclic matching counts of product graphs Pk×P2,Pk×P3,Pk×S1,m and graph classes Gk,Lk.In addition,the perfect matching counts of product graphs K4×Pn,K1,m×P2n,G×P4 are studied.