Result: Incidence matrices and line graphs of mixed graphs

Title:
Incidence matrices and line graphs of mixed graphs
Authors:
Mohammad Abudayah, Omar Alomari, Torsten Sander
Source:
Special Matrices, Vol 11, Iss 1, Pp 271-305 (2023)
Publication Status:
Preprint
Publisher Information:
Walter de Gruyter GmbH, 2023.
Publication Year:
2023
Subject Terms:
Cograph, Pathwidth, Degree matrix, Node (physics), 0102 computer and information sciences, mixed graph, Quantum mechanics, 01 natural sciences, Graph, Incidence matrix, Chordal graph, Comparability graph, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, 05C20, Graph Labeling and Dimension Problems, Graph power, Adjacency matrix, Physics, Graph Spectra and Topological Indices, Line graph, Indifference graph, Discrete mathematics, Block graph, line graph, Computational Theory and Mathematics, Combinatorics, hermitian adjacency matrix, Graph Theory, Physical Sciences, Computer Science, 05c22, Geometry and Topology, Combinatorics (math.CO), Mathematics, 05c20, Graph Theory and Algorithms
Document Type:
Academic journal Article<br />Other literature type
Language:
English
ISSN:
2300-7451
DOI:
10.1515/spma-2022-0176
DOI:
10.48550/arxiv.2205.05375
DOI:
10.60692/66qw9-wbq78
DOI:
10.60692/wnxe3-1m049
Access URL:
http://arxiv.org/abs/2205.05375
https://doaj.org/article/af8cc4e414a9461c96ef021419c249ed
Rights:
CC BY
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....d352dc7c2bc23b6dc44da16bf1b15bc5
Database:
OpenAIRE

Further Information

In the theory of line graphs of undirected graphs, there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, there exists no analogous result. The goal of this article is to present aligned definitions of the adjacency matrix, the incidence matrix, and line graph of a mixed graph such that the mentioned theorem is valid for mixed graphs.