The gamma-Signless Laplacian Adjacency Matrix of Mixed Graphs

Authors

Omar Alomari, College of Engineering and Technology, American University of the Middle East, KuwaitFollow
Mohammad Abudayah, German Jordanian UniversityFollow
Manal Ghanem, The University of JordanFollow

Abstract

The α-Hermitian adjacency matrix H_α of a mixed graph X has been recently introduced. It is a generalization of the adjacency matrix of unoriented graphs. In this paper, we consider a special case of the complex number α. This enables us to define an incidence matrix of mixed graphs. Consequently, we define a generalization of line graphs as well as a generalization of the signless Laplacian adjacency matrix of graphs. We then study the spectral properties of the gamma-signless Laplacian adjacency matrix of a mixed graph. Lastly, we characterize when the signless Laplacian adjacency matrix of a mixed graph is singular and give lower and upper bounds of number of arcs and digons in terms of largest and lowest eigenvalue of the signless Laplacian adjacency matrix.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Alomari, Omar; Abudayah, Mohammad; and Ghanem, Manal (2023) "The gamma-Signless Laplacian Adjacency Matrix of Mixed Graphs," Theory and Applications of Graphs: Vol. 10: Iss. 1, Article 11.
DOI: 10.20429/tag.2023.100111
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol10/iss1/11