Starlike tree

In the area of mathematics known as graph theory, a tree is said to be starlike if it has exactly one vertex of degree greater than 2. This high-degree vertex is the root and a starlike tree is obtained by attaching at least three linear graphs to this central vertex.

Properties[edit]

Two finite starlike trees are isospectral, i.e. their graph Laplacians have the same spectra, if and only if they are isomorphic.^[1] The graph Laplacian has always only one eigenvalue equal or greater than 4.^[2]

References[edit]

^ M. Lepovic, I. Gutman (2001). No starlike trees are cospectral.
^ 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.

External links[edit]

Weisstein, Eric W. "Spider Graph". MathWorld.
(sequence A004250 in the OEIS)

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[1] M. Lepovic, I. Gutman (2001). No starlike trees are cospectral.

[2] 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.

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