A new kind of $A_{\p}$-matrix for mixed graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911134334844928 |
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| author | Sharma, Piyush Kumar, Ravinder |
| author_facet | Sharma, Piyush Kumar, Ravinder |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_02326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new kind of $A_{\p}$-matrix for mixed graphs Sharma, Piyush Kumar, Ravinder Spectral Theory Combinatorics 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. |
| title | A new kind of $A_{\p}$-matrix for mixed graphs |
| topic | Spectral Theory Combinatorics |
| url | https://arxiv.org/abs/2509.02326 |