  Graphical passwords (GPWs) are convenient for mobile equipments with touch
screen. Topological graphic passwords (Topsnut-gpws) can be saved in computer
by classical matrices and run quickly than the existing GPWs. We research
Topsnut-gpws by the matching of view, since they have many advantages. We
discuss: configuration matching partition, coloring/labelling matching
partition, set matching partition, matching chain, etc. And, we introduce new
graph labellings for enriching Topsnut-matchings and show that these labellings
can be realized for trees or spanning trees of networks. In theoretical works
we explore Graph Labelling Analysis, and show that every graph admits our
extremal labellings and set-type labellings in graph theory. Many of the graph
labellings mentioned are related with problems of set matching partitions to
number theory, and yield new objects and new problems to graph theory.
