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
β¦ LIBER β¦
Structure of independent sets in direct products of some vertex-transitive graphs
β Scribed by Xing Bo Geng; Jun Wang; Hua Jun Zhang
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2011
- Tongue
- English
- Weight
- 219 KB
- Volume
- 28
- Category
- Article
- ISSN
- 1439-7617
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## 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
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