1. The gamma-Signless Laplacian Adjacency Matrix of Mixed Graphs
- Author
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Omar Alomari, Mohammad Abudayah, and Manal Ghanem
- Subjects
mixed graphs ,signless adjacency matrix ,hermitian adjacency matrix ,line graphs ,bipartite graphs ,Mathematics ,QA1-939 - Abstract
The α-Hermitian adjacency matrix Hα 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.
- Published
- 2023
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