A new kind of $A_{\p}$-matrix for mixed graphs
Spectral Theory
2025-09-03 v1 Combinatorics
Abstract
Nikiforov\cite{nikiforov2017merging} introduced the concept of the -matrix as a convex linear combination of a graph's adjacency matrix and its diagonal matrix of vertex degrees. In this paper, we introduce a new variant of the -matrix, which is a linear combination of the Hermitian adjacency matrix of the second kind, , and the degree-diagonal matrix. This study provides new insights into the -matrix as a Hermitian matrix, leading to novel bounds in spectral graph theory.
Keywords
Cite
@article{arxiv.2509.02326,
title = {A new kind of $A_{\p}$-matrix for mixed graphs},
author = {Piyush Sharma and Ravinder Kumar},
journal= {arXiv preprint arXiv:2509.02326},
year = {2025}
}