Incidence matrices and line graphs of mixed graphs-Reference-Cited by-同舟云学术

Incidence matrices and line graphs of mixed graphs

Published:2023-01-01 Issue:1 Volume:11 Page:
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Abudayah Mohammad¹,Alomari Omar¹,Sander Torsten²

Affiliation:

1. School of Basic Sciences and Humanities, German Jordanian University , Amman , Jordan

2. Fakultät für Informatik, Ostfalia Hochschule für angewandte Wissenschaften , Wolfenbüttel , Germany

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/spma-2022-0176/pdf

Reference21 articles.

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3. R. B. Bapat, Graphs and Matrices, Universitext, Springer, London, 2011.

4. D. M. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs. Theory and Applications, 3rd rev. a. enl. ed., J. A. Barth Verlag, Heidelberg, 1995.

5. K. Guo and B. Mohar, Hermitian adjacency matrix of digraphs and mixed graphs, J. Graph Theory 85 (2017), no. 1, 217–248.

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