Independence Ratio and Random Eigenvectors in Transitive Graphs
نویسنده
چکیده
1.1. The independence ratio and the minimum eigenvalue. An independent set is a set of vertices in a graph, no two of which are adjacent. The independence ratio of a graph G is the size of its largest independent set divided by the total number of vertices. If G is regular, then the independence ratio is at most 1/2, and it is equal to 1/2 if and only if G is bipartite. The adjacency matrix of a d-regular graph has real eigenvalues between −d and d. The least eigenvalue λmin is at least −d, and it is equal to −d if and only if the graph is bipartite.
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