Xiaogang Liu

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5 papers · 1 filter

math.CO2026

Index perturbation of signed graphs

Linfeng Xie, Xiaogang Liu

Let $Γ = (G, σ)$ be a signed graph and $v$ a non-isolated vertex of $Γ$ . Let $Γ - v$ denote the graph obtained by deleting the vertex $v$ together with all signed edges incident to it…

math.CO2026

Size and spectral conditions for a graph with given minimum degree to be $k$ - $d$ -critical

Zhenhao Zhang, Xiaogang Liu, Ligong Wang

A $k$ -matching in a graph $G$ is defined as a function $f : E (G) \to {0, 1, \dots, k}$ satisfying $\sum_{e \in E_{G} (v)} f (e)$ $\leq k$ for each vertex $v \in V (G)$ , where $E_G(v…

math.CO2026

Spectral Turán problem for $t K_{4}^{-}$ -free unbalanced signed graphs

Linfeng Xie, Xiaogang Liu

Let $t K_{4}$ denote the family of all graphs consisting of $t$ copies of $K_{4}$ that are allowed to share vertices and $t K_{4}^{-}$ be the set of all unbalanced signed graph…

math.CO2024

So's conjecture for integral circulant graphs of $4$ types

Hao Li, Xiaogang Liu

In [Discrete Mathematics 306 (2005) 153-158], So proposed a conjecture saying that integral circulant graphs with different connection sets have different spectra. This conjecture…

math.CO2024

Algebraic degrees of $n$ -Cayley digraphs over abelian groups

Hao Li, Xiaogang Liu

A digraph is called an $n$ -Cayley digraph if its automorphism group has an $n$ -orbit semiregular subgroup. We determine the splitting fields of $n$ -Cayley digraphs over abelian gro…

Index perturbation of signed graphs

Size and spectral conditions for a graph with given minimum degree to be k-d-critical

Spectral Turán problem for tK4−​-free unbalanced signed graphs

So's conjecture for integral circulant graphs of 4 types

Algebraic degrees of n-Cayley digraphs over abelian groups

Size and spectral conditions for a graph with given minimum degree to be $k$ - $d$ -critical

Spectral Turán problem for $t K_{4}^{-}$ -free unbalanced signed graphs

So's conjecture for integral circulant graphs of $4$ types

Algebraic degrees of $n$ -Cayley digraphs over abelian groups