Limit points of eigenvalues of (di)graphs

Zhang, Fu Ji, and Chen, Zhibo. "Limit points of eigenvalues of (di)graphs." Czechoslovak Mathematical Journal 56.3 (2006): 895-902. <http://eudml.org/doc/31075>.

@article{Zhang2006,
abstract = {The study on limit points of eigenvalues of undirected graphs was initiated by A. J. Hoffman in 1972. Now we extend the study to digraphs. We prove: 1. Every real number is a limit point of eigenvalues of graphs. Every complex number is a limit point of eigenvalues of digraphs. 2. For a digraph $D$, the set of limit points of eigenvalues of iterated subdivision digraphs of $D$ is the unit circle in the complex plane if and only if $D$ has a directed cycle. 3. Every limit point of eigenvalues of a set $\mathcal \{D\}$ of digraphs (graphs) is a limit point of eigenvalues of a set $\ddot\{\mathcal \{D\}\}$ of bipartite digraphs (graphs), where $\ddot\{\mathcal \{D\}\}$ consists of the double covers of the members in $\mathcal \{D\}$. 4. Every limit point of eigenvalues of a set $\mathcal \{D\}$ of digraphs is a limit point of eigenvalues of line digraphs of the digraphs in $\mathcal \{D\}$. 5. If $M$ is a limit point of the largest eigenvalues of graphs, then $-M$ is a limit point of the smallest eigenvalues of graphs.},
author = {Zhang, Fu Ji, Chen, Zhibo},
journal = {Czechoslovak Mathematical Journal},
keywords = {limit point; eigenvalue of digraph (graph); double cover; subdivision digraph; line digraph; limit point; eigenvalue of digraph (graph); double cover; subdivision digraph; line digraph},
language = {eng},
number = {3},
pages = {895-902},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Limit points of eigenvalues of (di)graphs},
url = {http://eudml.org/doc/31075},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Zhang, Fu Ji
AU - Chen, Zhibo
TI - Limit points of eigenvalues of (di)graphs
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 895
EP - 902
AB - The study on limit points of eigenvalues of undirected graphs was initiated by A. J. Hoffman in 1972. Now we extend the study to digraphs. We prove: 1. Every real number is a limit point of eigenvalues of graphs. Every complex number is a limit point of eigenvalues of digraphs. 2. For a digraph $D$, the set of limit points of eigenvalues of iterated subdivision digraphs of $D$ is the unit circle in the complex plane if and only if $D$ has a directed cycle. 3. Every limit point of eigenvalues of a set $\mathcal {D}$ of digraphs (graphs) is a limit point of eigenvalues of a set $\ddot{\mathcal {D}}$ of bipartite digraphs (graphs), where $\ddot{\mathcal {D}}$ consists of the double covers of the members in $\mathcal {D}$. 4. Every limit point of eigenvalues of a set $\mathcal {D}$ of digraphs is a limit point of eigenvalues of line digraphs of the digraphs in $\mathcal {D}$. 5. If $M$ is a limit point of the largest eigenvalues of graphs, then $-M$ is a limit point of the smallest eigenvalues of graphs.
LA - eng
KW - limit point; eigenvalue of digraph (graph); double cover; subdivision digraph; line digraph; limit point; eigenvalue of digraph (graph); double cover; subdivision digraph; line digraph
UR - http://eudml.org/doc/31075
ER -