A spectral faux tree with respect to a given matrix is a graph which is not a tree but is cospectral with a tree for the given matrix. We consider the existence of spectral faux trees for several matrices, with emphasis on constructions. For the Laplacian matrix, there are no spectral faux trees. For the adjacency matrix, almost all trees are cospectral with a faux tree. For the signless Laplacian matrix, spectral faux trees can only exist when the number of vertices is of the form $n=4k$. For the normalized adjacency, spectral faux trees exist when the number of vertices $n\ge 4$, and we give an explicit construction for a family whose size grows exponentially with $k$ for $n=\alpha k+1$ where $\alpha$ is fixed.Comment: 17 page
We classify the trees for which there is a nonsingular matrix where each vertex is a P-vertex. In pa...
Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenve...
Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenve...
For the normalized Laplacian matrix it is possible for graphs with differing number of edges to have...
AbstractIn this paper, we show that if G is a starlike tree, then it is determined by its Laplacian ...
If $G$ is a graph and $\mathbf{m}$ is an ordered multiplicity list which is realizable by at least o...
Abstract Background There are several common ways to encode a tree as a matrix, such as the adjacenc...
In [E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Ap...
Abstract Background There are several common ways to encode a tree as a matrix, such as the adjacenc...
Spectral problems are considered generated by the Sturm-Liouville equation on equilateral trees with...
We survey properties of spectra of signless Laplacians of graphs and discuss possibilities for devel...
We classify the trees for which there is a nonsingular matrix where each vertex is a P-vertex. In pa...
In this thesis we look at various tools to analyse eigenvalues and eigenvectors and use themto prove...
We survey properties of spectra of signless Laplacians of graphs and discuss possibilities for devel...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.Includes bibliogr...
We classify the trees for which there is a nonsingular matrix where each vertex is a P-vertex. In pa...
Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenve...
Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenve...
For the normalized Laplacian matrix it is possible for graphs with differing number of edges to have...
AbstractIn this paper, we show that if G is a starlike tree, then it is determined by its Laplacian ...
If $G$ is a graph and $\mathbf{m}$ is an ordered multiplicity list which is realizable by at least o...
Abstract Background There are several common ways to encode a tree as a matrix, such as the adjacenc...
In [E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Ap...
Abstract Background There are several common ways to encode a tree as a matrix, such as the adjacenc...
Spectral problems are considered generated by the Sturm-Liouville equation on equilateral trees with...
We survey properties of spectra of signless Laplacians of graphs and discuss possibilities for devel...
We classify the trees for which there is a nonsingular matrix where each vertex is a P-vertex. In pa...
In this thesis we look at various tools to analyse eigenvalues and eigenvectors and use themto prove...
We survey properties of spectra of signless Laplacians of graphs and discuss possibilities for devel...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.Includes bibliogr...
We classify the trees for which there is a nonsingular matrix where each vertex is a P-vertex. In pa...
Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenve...
Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenve...