TY - JOUR
T1 - On the Laplacian spread of digraphs
AU - Barrett, Wayne
AU - Cameron, Thomas R.
AU - Evans, Emily
AU - Hall, H. Tracy
AU - Kempton, Mark
N1 - Funding Information:
This work was supported by the AMS-Simons Travel Grants, which are administered by the American Mathematical Society with support from the Simons Foundation .
Publisher Copyright:
© 2023 Elsevier Inc.
PY - 2023/5/1
Y1 - 2023/5/1
N2 - In this article, we extend the notion of the Laplacian spread to simple directed graphs (digraphs) using the restricted numerical range. First, we provide Laplacian spread values for several families of digraphs. Then, we prove sharp upper bounds on the Laplacian spread for all polygonal and balanced digraphs. In particular, we show that the validity of the Laplacian spread bound for balanced digraphs is equivalent to the Laplacian spread conjecture for simple undirected graphs, which was conjectured in 2011 and proven in 2021. Moreover, we prove an equivalent statement for weighted balanced digraphs with weights between 0 and 1. Finally, we state several open conjectures that are motivated by empirical data.
AB - In this article, we extend the notion of the Laplacian spread to simple directed graphs (digraphs) using the restricted numerical range. First, we provide Laplacian spread values for several families of digraphs. Then, we prove sharp upper bounds on the Laplacian spread for all polygonal and balanced digraphs. In particular, we show that the validity of the Laplacian spread bound for balanced digraphs is equivalent to the Laplacian spread conjecture for simple undirected graphs, which was conjectured in 2011 and proven in 2021. Moreover, we prove an equivalent statement for weighted balanced digraphs with weights between 0 and 1. Finally, we state several open conjectures that are motivated by empirical data.
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U2 - 10.1016/j.laa.2023.01.016
DO - 10.1016/j.laa.2023.01.016
M3 - Article
AN - SCOPUS:85147249913
SN - 0024-3795
VL - 664
SP - 126
EP - 146
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -