# An Efficient Algorithm for Graph Isomorphism

@article{Corneil1970AnEA, title={An Efficient Algorithm for Graph Isomorphism}, author={Derek G. Corneil and Calvin C. Gotlieb}, journal={J. ACM}, year={1970}, volume={17}, pages={51-64} }

A procedure for determining whether two graphs are isomorphic is described. During the procedure, from any given graph two graphs, the representative graph and the reordered graph, are derived. The representative graph is a homomorphic image of the original graph; the reordered graph is constructed from the representative graph to be isomorphic to the given graph. Unique labels are assigned to the vertices of both derived graphs. It follows that two repre- sentative graphs or two reordered…

## 342 Citations

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## References

SHOWING 1-10 OF 12 REFERENCES

### Algorithms for finding a fundamental set of cycles for an undirected linear graph

- Computer ScienceCACM
- 1967

The algorithm presented in this paper finds a spanning tree and then constructs the set of fundamental cycles and is slower than an algorithm presented by Welch by a ratio of N/3 (N is the number of nodes) but requires less storage.

### Strongly regular graphs, partial geometries and partially balanced designs.

- Mathematics
- 1963

This paper introduces the concept of a partial geometry, which serves to unify and generalize certain theorems on embedding of nets, and uniqueness of association schemes of partially balanced…

### Orthogonal Matrices with Zero Diagonal

- MathematicsCanadian Journal of Mathematics
- 1967

The central problem in the present paper is the construction of symmetric and of skew-symmetric ( = skew) matrices C of order v, with diagonal elements 0 and other elements + 1 or — 1, satisfying The…

### Storage and retrieval of information on chemical structures by computer.

- Chemistry, MedicineEndeavour
- 1968

### GIT—a heuristic program for testing pairs of directed line graphs for isomorphism

- Computer ScienceCACM
- 1964

GIT—Graph Isomorphism Tester—incorporates a variety of processes that attempt to narrow down the search for an isomorphism, or to demonstrate that none exists.