Xueyi Huang

Eigenvalue bounds for combinatorial Laplacians and an application to random complexes

Xiongfeng Zhan, Xueyi Huang, Jin-Xin Zhou

This paper establishes new eigenvalue bounds for combinatorial Laplacians of simplicial complexes, extending previous results for flag complexes by Lew (2024) and general complexes…

Combinatorial Laplacians and Relative Homology of Complex Pairs

Xiongfeng Zhan, Xueyi Huang, Lu Lu

As a discretization of the Hodge Laplacian, the combinatorial Laplacian of simplicial complexes has garnered significant attention. In this paper, we study combinatorial Laplacians…

A note on the Björner--Kalai theorem

Xiongfeng Zhan, Xueyi Huang

In 1988, Björner and Kalai used combinatorial shadow functions to characterize the maximal Betti sequence for a given $f$ -vector and the minimal $f$ -vector for a given Betti sequen…

Fractional revival on quasi-abelian Cayley graphs

Yi Fang, Xueyi Huang, Xiaogang Liu +1

Fractional revival, a quantum transport phenomenon critical to entanglement generation in quantum spin networks, generalizes the notion of perfect state transfer on graphs. A Cayle…

An Extension of Pólya's Enumeration Theorem

Xiongfeng Zhan, Xueyi Huang

In combinatorics, Pólya's Enumeration Theorem is a powerful tool for solving a wide range of counting problems, including the enumeration of groups, graphs, and chemical compounds.…

Proof of Lew's conjecture on the spectral gaps of simplicial complexes

Xiongfeng Zhan, Xueyi Huang, Huiqiu Lin

As a generalization of graph Laplacians to higher dimensions, the combinatorial Laplacians of simplicial complexes have garnered increasing attention. Let $X$ be a simplicial compl…

Fourier analysis on distance-regular Cayley graphs over abelian groups

Xiongfeng Zhan, Xueyi Huang, Lu Lu

The problem of constructing or characterizing strongly regular Cayley graphs (or equivalently, regular partial difference sets) has garnered significant attention over the past hal…

On the spectral extremal problem of planar graphs

Xiaolong Wang, Xueyi Huang, Huiqiu Lin

The spectral extremal problem of planar graphs has aroused a lot of interest over the past three decades. In 1991, Boots and Royle [Geogr. Anal. 23(3) (1991) 276--282] (and Cao and…

math.CO2023

Distance-regular Cayley graphs over (pseudo-) semi-dihedral groups

Xueyi Huang, Lu Lu, Xiongfeng Zhan

Distance-regular graphs are a class of regualr graphs with pretty combinatorial symmetry. In 2007, Miklavič and Potočnik proposed the problem of charaterizing distance-regular Cayl…

math.CO2023

Distance-regular Cayley graphs over $Z_{p^{s}} \oplus Z_{p}$

Xiongfeng Zhan, Lu Lu, Xueyi Huang

In [Distrance-regular Cayley graphs on dihedral groups, J. Combin. Theory Ser B 97 (2007) 14--33], Miklavič and Potočnik proposed the problem of characterizing distance-regular Cay…

math.CO2023★ 2 cited

Spectral condition for spanning $k$ -ended trees in $t$ -connected graphs

Jiaxin Zheng, Xueyi Huang, Junjie Wang

For any integer $k \geq 2$ , a spanning $k$ -ended tree is a spanning tree with at most $k$ leaves. In this paper, we provide a tight spectral radius condition for the existence of a…

math.CO2023

Toughness and normalized Laplacian eigenvalues of graphs

Xueyi Huang, Kinkar Chandra Das, Shunlai Zhu

Given a connected graph $G$ , the toughness $τ_{G}$ is defined as the minimum value of the ratio $∣ S ∣/ ω_{G - S}$ , where $S$ ranges over all vertex cut sets of $G$ , and $ω_{G - S}$ is the…

Spectral conditions for graphs having all (fractional) $[a, b]$ -factors

Jiaxin Zheng, Junjie Wang, Xueyi Huang

Let $a \leq b$ be two positive integers. We say that a graph $G$ has all $[a, b]$ -factors if it has an $h$ -factor for every function $h : V (G) \to Z^{+}$ such that $a\le…

On directed strongly regular Cayley graphs over non-abelian groups with an abelian subgroup of index $2$

Xueyi Huang, Lu Lu, Jongyook Park

In 1988, Duval introduced the concept of directed strongly regular graphs, which can be viewed as a directed graph version of strongly regular graphs. Such directed graphs have sim…

math.CO2022★ 1 cited

Spectral radius of graphs with given size and odd girth

Zhenzhen Lou, Lu Lu, Xueyi Huang

Let $G (m, k)$ be the set of graphs with size $m$ and odd girth (the length of shortest odd cycle) $k$ . In this paper, we determine the graph maximizing the spectral radius…

Spectral radius and (globally) rigidity of graphs in $R^{2}$

Dandan Fan, Xueyi Huang, Huiqiu Lin

Over the past half century, the rigidity of graphs in $R^{2}$ has aroused a great deal of interest. Lovász and Yemini (1982) proved that every $6$ -connected graph is rigid in $R^{2}$ .…

Distance-regular Cayley graphs over dicyclic groups

Xueyi Huang, Kinkar Chandra Das, Lu Lu

The characterization of distance-regular Cayley graphs originated from the problem of identifying strongly regular Cayley graphs, or equivalently, regular partial difference sets.…

Splitting fields of mixed Cayley graphs over abelian groups

Xueyi Huang, Lu Lu, Katja Mönius

The splitting field $SF (Γ)$ of a mixed graph $Γ$ is the smallest field extension of $Q$ which contains all eigenvalues of the Hermitian adjacency matrix of $Γ$ . T…