Starlike tree

<h2 id="properties">Properties</h2>
<p>Two finite starlike trees are <a href="/facts/Isospectral/vvYRzPqT">isospectral</a>, i.e. their <a href="/facts/Discrete_Laplace_operator/w3fdFNC4">graph Laplacians</a> have the same spectra, if and only if they are <a href="/facts/Graph_isomorphism/SBjVIhwW">isomorphic</a>.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a>  The graph Laplacian has always only one eigenvalue equal or greater than 4.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
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<h2 id="external-links">External links</h2>
<ul><li><a href="/facts/Eric_W._Weisstein/FbMuVDep">Weisstein, Eric W.</a> <a href="https://mathworld.wolfram.com/SpiderGraph.html">"Spider Graph"</a>. <i><a href="/facts/MathWorld/yc1jodbq">MathWorld</a></i>.</li>
<li>(sequence A004250 in the <a href="/facts/On-Line_Encyclopedia_of_Integer_Sequences/yow6cVsU">OEIS</a>)</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>M. Lepovic, I. Gutman (2001). No starlike trees are cospectral. <a href="https://www.sciencedirect.com/science/article/pii/S0012365X01001698" target="_blank">https://www.sciencedirect.com/science/article/pii/S0012365X01001698</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Nakatsukasa, Yuji; Saito, Naoki; Woei, Ernest (April 2013). "Mysteries around the Graph Laplacian Eigenvalue 4". Linear Algebra and Its Applications. 438 (8): 3231–46. arXiv:1112.4526. doi:10.1016/j.laa.2012.12.012. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
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Starlike tree open-in-new

Starlike tree