Measuring tree structure by mapping on its power set

In pattern recognition, graphs as structural pattern representations become alluring more and more due to their richer representability than those of feature vectors. However, there are many challenging problems in using graphs for pattern recognition. One is how to exploit so much information efficiently, such as labels, weights, directions, relationships and structures included in a graph. In this paper, we focus on the structure problem of graphs, especially tree isomorphism, which is almost suffered from all kinds of graph matching problems. One of the reasons of the difficulty to deal with the structure of graphs is the heterogeneity that two different kinds of information exist concurrently: vertex and edge. To overcome this difficulty, we propose a homogeneous representation for a graph by mapping a graph to the subset of its vertex power set by preserving the connectivity, i.e. edge information. Based on this representation, we propose a numeric sequence to represent the structure of a graph, and illustrate the efficiency on the tree isomorphism problem.