Let G be a unicyclic graph on n >= 3 vertices. Let A(G) be the adjacency matrix of G. The eigenvalues of A(G) are denoted by lambda(1)(G) >= lambda(2)(G) >= ... >= lambda(n)(G), which are called the eigenvalues of G. Let the unicyclic graphs G on n vertices be ordered by their least eigenvalues lambda(n)(G) in non-decreasing order. For n >= 14, the first six graphs in this order are determined.
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