Author

Chaochao Zhu

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Preprint Sep 2026

A Characterization of Walk-Matrix Equivalence at Corank Two via Reciprocal WQH Switching

Let $G$ be a graph of order $n$ with adjacency matrix $A_G$, let $\mathbf e$ denote the all-one vector, and let$W_G=[\mathbf e,A_G\mathbf e,\ldots,A_G^{n-1}\mathbf e]$ be its walk matrix. We consider the case $\operatorname{rank}W_G=n-2$, the first corank for which distinct graphs can have the same walk matrix. We give...

Chao-Chao Zhu, Q. Yue · 0 citations

Preprint Aug 2026

A Sharp Matching-Number Threshold for Spectral-Walk Determination of Trees

The spectral characterization of graphs is a central problem in spectral graph theory. In this paper we study when a tree is determined, among trees, by its generalized spectrum. We use the equivalent formulation given by the adjacency spectrum together with the total-walk sequence $W_k(G)=\mathbf 1^{\mathsf T}A(G)^k\m...

Chao-Chao Zhu · 1 citation