Spectral Solution for Detecting Isomorphic Graphs with Nondegenerate Eigenvalues

Graph Isomorphism (GI) is to find a bijection between the vertices of two graphs G
₁
and G
₂
, such that any two vertices in G
₁
are adjacent if they are adjacent in G
₂
. There are several application areas in which graph isomorphism is required, such as study of organic compounds isomers, algorithms' similarity analysis in profiling of Embedded Systems, VLSI circuits equivalence etc. The complexity of Graph Isomorphism problem is thought neither to be in P nor in NP-Complete although this has not been proved yet [1], [2]. We classify the graph on the basis of their Adjacency Matrix (AM) eigenvalues. A Non- degenerate eigenvalue corresponds to a distinct eigenvector instead of a subspace as in the case of degeneracy, making the problem simpler. We employ spectral decomposition of AM for finding a solution. Furthermore, we redefine the isomorphic transform equation by including eigenvectors into it. Index