## Given an n-dimensional point-lattice A c [w" and a bounded set A c KY, the set S(A) of nonzero lattice points ueA such that A n (A + u) # f~ is called the set of neighbours of A in ,4. In the paper a disjoint decomposition of S(A) is showed which gives a representation of the cardinality N(A) o
Transitivity on sets of independent points in geometric lattices
β Scribed by Anne Delandtsheer
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 177 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
## 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
## Abstract A maximal independent set of a graph __G__ is an independent set that is not contained properly in any other independent set of __G__. Let __i(G)__ denote the number of maximal independent sets of __G__. Here, we prove two conjectures, suggested by P. ErdΓΆs, that the maximum number of m