Hechao Liu

collaborators

3 papers

math.CO2026

Signed graphs with exactly two main eigenvalues: The unicyclic case

Zenan Du, Fenjin Liu, Hechao Liu +2

An eigenvalue $I^»$ of a signed graph $S$ of order $n$ is called a main eigenvalue if its eigenspace is not orthogonal to the all-ones vector $j$ . Characterizing signed graphs with…

math.CO2025

Signless Laplacian spectral conditions for even factors in graphs

Lu Li, Hechao Liu, Hongbo Hua +1

A spanning subgraph $F$ of a graph $G$ is defined as an even factor of $G$ , if the degree $d_{F} (v) = 2 k, k \in N^{+}$ for every vertex $v \in V (G)$ . This note establishes a suffic…

math.CO2025

Enumeration of spanning trees and resistance distances of generalized blow-up graphs

Hechao Liu, Lu Li, Lihua You +2

Let $H$ be a graph with vertex set $V (H) = {v_{1}, v_{2}, \dots, v_{k}}$ . The generalized blow-up graph $H_{p_{1}, \dots, p_{k}}^{q_{1}, \dots, q_{k}}$ is constructed by replacing each vertex $v_…