Abstract: Using the design idea of the structure of graphs and number theory, we applied the labelling to the study of graphical password, gave and proved the setordered graceful labelling, the strongly graceful labelling, properties of some vertices and the oddgraceful labelling which was formed by adding the leaves of each vertex.

Key words: setordered graceful labelling, strongly graceful labelling, hierarchicalgraph, oddgraceful labelling, graphical password