New matrices for the spectral theory of mixed graphs, part I
Combinatorics
2025-11-27 v2 Spectral Theory
Abstract
In this paper, we introduce a matrix for a mixed graph, called the integrated adjacency matrix. This matrix uniquely determines a mixed graph, as long as the indices of the matrix are specified. Additionally, we associate an (undirected) graph with each mixed graph, enabling the spectral analysis of the integrated adjacency matrix to connect the structural properties of the mixed graph and its associated graph. Furthermore, we define certain mixed graph structures and establish their relationships to the eigenvalues of the integrated adjacency matrix.
Cite
@article{arxiv.2411.19879,
title = {New matrices for the spectral theory of mixed graphs, part I},
author = {G. Kalaivani and R. Rajkumar},
journal= {arXiv preprint arXiv:2411.19879},
year = {2025}
}
Comments
34 pages, 7 figures (Accepted version in Journal)