Abstract: Using  the design idea of  the structure of graphs and number theory, the graph labelling was  applied to the  graphical cryptograph. The hierarchical cascade graph was used as the basic graph, which was  connected with cycle graph to  construct a unicyche graph, and then the two hierarchical cascade  graphs were overlapped to construct the twin vertex overlap graph. We proved that it has set-ordered odd-elegant labellings, odd-graceful labelling and set-ordered odd-graceful labelling.

Key words: graphical password, hierarchicalgraph, unicyclic graph, twin vertexidentified graph