A new kind of $A_{\p}$-matrix for mixed graphs

Piyush Sharma; Ravinder Kumar

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arXiv · 2509.02326

A new kind of $A_{\p}$-matrix for mixed graphs

Piyush Sharma·Ravinder Kumar

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Abstract

Nikiforov\cite{nikiforov2017merging} introduced the concept of the $A_{\p}$-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 $A_{\p}$-matrix, which is a linear combination of the Hermitian adjacency matrix of the second kind, $H^{\om}$, and the degree-diagonal matrix. This study provides new insights into the $A_{\p}$-matrix as a Hermitian matrix, leading to novel bounds in spectral graph theory.

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BibTeX RIS

Piyush Sharma, Ravinder Kumar. 2025-09-02. A new kind of $A_{\p}$-matrix for mixed graphs. https://arxiv.org/abs/2509.02326

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