Graph Isomorphism-Characterization and Efficient Algorithms

The graph isomorphism problem involves determining whether two graphs are isomorphic and the computational complexity required for this determination. In general, the problem is not known to be solvable in polynomial time, nor to be NP-complete. In this paper, we prove that for undirected graphs, the complexity in determining whether two graphs are isomorphic is at most $\mathcal{O}(n^{3})$.