On the spectral characterization of T-shape trees

By Wei Wang, Cheng-Xian Xu. 2006

65 citations recorded by the source corpus.

A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is isomorphic to G. A T-shape is a tree with exactly one of its vertices having maximal degree 3. In this paper, we show that all T-shape trees are determined by their spectra, except for a few well-defined cases.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d85396358f893396fa54bf0bf8c0f050badda1df

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Towards a spectral theory of graphs based on the signless Laplacian, III (2010, background): “As demonstrated in the first part, the Q–theory can be constructed in part using various connections to other theories: equivalence with A–theory and L–theory for regular graphs, common features with L–theory for bipartite graphs, general analogies with A–theory and analogies with A–theory via line ”
Towards a spectral theory of graphs based on the signless Laplacian, I (2009, background): “[50].”
Discrete mathematics (2004, unknown): “Exclusive or: p ⊕ q is true when exactly one of p and q is true, and false otherwise Truth table: Instructor:I¸sılDillig, CS311H:DiscreteMathematics Introand PropositionalLogic 25/36”
Starlike trees are determined by their Laplacian spectrum (2007, background): “Also in [10] it was proved that T (l1, l2, l3) is determined by its adjacency spectrum if and only if (l1, l2, l3) / = (l, l, 2l − 2) for any integer l 2.”
Spectral characterizations of lollipop graphs (2008, unknown): “The following known results can be found in [2,3,7,8,11,12,13,14].”