Author

Zhen-Mu Hong

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Preprint Sep 2026

A proof of the resistance diameter conjecture for line graphs

We prove the conjecture of Xu, Li, Hua, and Pan that the resistance diameter does not increase under the line-graph operation. For every finite connected simple graph $G$ with at least one edge, we establish $D_r(L(G))\le D_r(G)$, with equality if and only if $G$ is a cycle or $K_4$. The proof combines an exact electri...

Xiang-Feng Pan, Xiang-Yang Liu, Zhen-Mu Hong · 0 citations

Preprint Oct 2026

Graph Sensitivity of Cartesian Products with Matched Bridges

For a graph $G$, let $f_t(G)$ denote the minimum of the maximum degree of an induced subgraph with $\alpha(G)+t$ vertices, where $\alpha(G)$ is the independence number, and write $f(G)=f_1(G)$. Huang's theorem gives $f(Q_k)\ge\lceil\sqrt{k}\rceil$ for the $k$-dimensional hypercube $Q_k$. We extend this lower bound to C...

Zhen-Mu Hong, Zi-Yi Wu, Zheng-Jiang Xia · 0 citations