1. Graphs isomorphic to their path graphs
- Creator:
- Knor, Martin and Niepel, Ľudovít
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- line graph, path graph, and cycles
- Language:
- English
- Description:
- We prove that for every number n ≥ 1, the n-iterated P3-path graph of G is isomorphic to G if and only if G is a collection of cycles, each of length at least 4. Hence, G is isomorphic to P3(G) if and only if G is a collection of cycles, each of length at least 4. Moreover, for k ≥ 4 we reduce the problem of characterizing graphs G such that Pk(G) ∼= G to graphs without cycles of length exceeding k.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public