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Title: Determining Levels of Detail for Simulators of Parallel and Distributed Computing Systems via Automated Calibration
Award ID(s):
2411154 2106059 2103489 2106147
PAR ID:
10647224
Author(s) / Creator(s):
; ; ; ; ; ; ;
Publisher / Repository:
ACM
Date Published:
Page Range / eLocation ID:
1452 to 1463
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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    A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the new distance matrix, with natural extensions to the distance Laplacian and distance signless Laplacian, in addition to the new adjacency matrix, with natural extensions to the Laplacian and signless Laplacian. Various sums of Kronecker products of nonnegative matrices are introduced to model the Cartesian and lexicographic products of digraphs. The Jordan canonical form is applied extensively to the analysis of spectra and eigenvectors. The analysis shows that Cartesian products provide a method for building infinite families of transmission regular digraphs with few distinct distance eigenvalues. 
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