On Multiple Eigenvalues of Trees
نویسنده
چکیده
Let T be a tree of order n > 6 with μ as a positive eigenvalue of multiplicity k. Star complements are used to show that (i) if k > n/3 then μ = 1, (ii) if μ = 1 then, without restriction on k, T has k+ 1 pendant edges that form an induced matching. The results are used to identify the trees with a non-zero eigenvalue of maximum possible multiplicity.
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