首页|A note on the multiplicities of the eigenvalues of a tree
A note on the multiplicities of the eigenvalues of a tree
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NSTL
Elsevier
? 2022 Elsevier Inc.Let T be a tree of order n with μ as an eigenvalue of multiplicity mT(μ). Wong et al. showed that [Formula presented] when n>6 and μ2 is an integer at least 2. In this paper, we generalize this result by first showing that if T is a tree of order n and t is a positve integer, then (i) if n≤2t+2, then mT(t)≤1; (ii) If n≥2t+3, then [Formula presented], with equality if and only if T has a vertex v such that T?v=kK1,t for some integer k≥2.
Eigenvalue multiplicityStar complementTree
Zhang Y.、Zhou Q.、Wong D.
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School of Mathematics China University of Mining and Technology
NSTL
Elsevier
