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Fowler, Patrick W.


Graph Theory » Algebraic G.T.

Fowler's Conjecture on eigenvalues of (3,6)-polyhedra ★★

Author(s): Fowler

Conjecture   Let $ G $ be the graph of a $ (3,6) $-polyhedron with $ 2k + 4 $ vertices. Then the eigenvalues of $ G $ can be partitioned into three classes: $ K = \{3, -1, -1, -1\} $, $ P = {x_1, ..., x_k\} $ (where $ x_i $ is nonnegative for $ i = 1, \dots , k $), and $ N = - P $.

Keywords: (3,6)-polyhedron; eigenvalues

Posted by Robert Samal
updated April 8th, 2008
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