## Seminar:

Fall 2017, Thursdays, Blocker 628, 4:00-4:50 PM
__ Date:__ ** October 26 **

**" Effective Resistance Preserving Isomorphism "**

**Byeongsu Yu**

__Abstract__This presentation introduces the concept of an effective resistance and the effective resistance preserving isomorphism between two graphs. Then it shows that every subgraph isomorphism of two trees is the effective resistance preserving isomorphism. Moreover, it introduced a binary operation for two finite connected unweighted graphs G and H, called attaching H to G as a wing. This operation induces the canonical subgraph isomorphism between G and the resultant graph from the operation. For the finite connected unweighted graph G and H, we prove that the canonical subgraph isomorphism is the effective resistance preserving isomorphism up to a scalar.