We introduce the concept of the primitivity of independent set in vertex-transitive graphs, and investigate the relationship between the primitivity and the structure of maximum independent sets in direct products of vertex-transitive graphs. As a consequence of our main results, we positively solve
Independent sets in direct products of vertex-transitive graphs
β Scribed by Huajun Zhang
- Book ID
- 113698926
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 147 KB
- Volume
- 102
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let __G__ be a connected, nonbipartite vertexβtransitive graph. We prove that if the only independent sets of maximal cardinality in the tensor product __G__ Γ __G__ are the preimages of the independent sets of maximal cardinality in __G__ under projections, then the same holds for all
Let G be an undirected connected graph with n nodes. A subset F of nodes of G is a feedback vertex set (fvs) if G -F is a forest and a subset J of nodes of G is a nonseparating independent set (nsis) if no two nodes of J are adjacent and G -J is connected. f(G), z ( G ) denote the cardinalities of a