Jin-Xin Zhou

activity

20162026

most citedOn

k

-connected-homogeneous graphs

5 citations · 26 across the 37 of their papers we have counts for

collaborators

38 papers

math.GR2026

Enumeration of orientably-regular maps with automorphism group $\PGam(2,2^p)$ for prime $p$

Yan-Quan Feng, Soňa Pavlíková, Jozef Širáň +2

With help of group characters we enumerate orientably-regular maps of a given type with automorphism group isomorphic to $\PGam(2,2^p)$ for prime $p$ .

math.CO2026

A transfer principle for Steklov eigenvalue estimates of graphs

Xiongfeng Zhan, Jin-Xin Zhou

In this paper, we establish a new variant of the Burger-Brooks transfer principle, which allows us to apply spectral estimates for measured Riemannian surfaces to obtain the follow…

math.GR2026

The finite $k$ -set homogeneous graphs

Cai Heng Li, Fu-Gang Yin, Jin-Xin Zhou

A classification is given of finite $k$ -set-homogeneous graphs for $k ⩾ 2$ , leading to a striking result that each finite $k$ -set-homogeneous graph is $k$ -homogeneous. It sh…

math.GR2025

On automorphism groups of half-arc-transitive tetravalent graphs

Yuandong Li, Binzhou Xia, Jin-Xin Zhou

We characterize connected tetravalent graphs $Γ$ which admit groups $M < H$ of automorphisms such that $Γ$ is $M$ -half-arc-transitive and $H$ -arc-transitive. Examples for each case a…

math.CO2025

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…

math.CO2025

On tetravalent half-arc-transitive graphs

Jin-Xin Zhou

Vertex-stabilizers of trivalent edge-transitive graphs have been classified by Tutte, Goldschmidt and some others in several previous papers. Tetravalent half-arc-transitive graphs…

math.CO2025

On kernel isomorphisms of $m$ -Cayley digraphs and finite $2$ PCI-groups

Xing Zhang, Yan-Quan Feng, Jin-Xin Zhou +1

The isomorphism problem for digraphs is a fundamental problem in graph theory. In this paper, we consider this problem for $m$ -Cayley digraphs which are generalization of Cayley di…

math.GR2025

Normal and non-normal Cayley digraphs on cyclic and dihedral groups

Jun-Feng Yang, Yan-Quan Feng, Fu-Gang Yin +1

A Cayley digraph on a group $G$ is called NNN if the Cayley digraph is normal and its automorphism group contains a non-normal regular subgroup isomorphic to $G$ . A group is called…

math.CO2024

On isomorphisms of $m$ -Cayley digraphs

Xing Zhang, Yuan-Quan Feng, Fu-Gang Yin +1

The isomorphism problem for digraphs is a fundamental problem in graph theory. This problem for Cayley digraphs has been extensively investigated over the last half a century. In t…

math.CO2024

The classification of two-distance transitive dihedrants

Jun-Jie Huang, Yan-Quan Feng, Jin-Xin Zhou +1

A vertex transitive graph $Γ$ is said to be $2$ -distance transitive if for each vertex $u$ , the group of automorphisms of $Γ$ fixing the vertex $u$ acts transitively on the set of…

math.GR2023

Quasiprimitive groups with a biregular dihedral subgroup,and arc-transitive bidihedrants

Jiangmin Pan, Fu-Gang Yin, Jin-Xin Zhou

A semiregular permutation group on a set $\Ome$ is called {\em bi-regular} if it has two orbits. A classification is given of quasiprimitive permutation groups with a biregular dih…

math.CO2023

Using mixed dihedral groups to construct normal Cayley graphs, and a new bipartite $2$ -arc-transitive graph which is not a Cayley graph

Daniel R. Hawtin, Cheryl E. Praeger, Jin-Xin Zhou

A \emph{mixed dihedral group} is a group $H$ with two disjoint subgroups $X$ and $Y$ , each elementary abelian of order $2^{n}$ , such that $H$ is generated by $X \cup Y$ , and $H/H'\con…

math.CO2023

A family of $2$ -groups and an associated family of semisymmetric, locally $2$ -arc-transitive graphs

Daniel R. Hawtin, Jin-Xin Zhou, Cheryl E. Praeger

A mixed dihedral group is a group $H$ with two disjoint subgroups $X$ and $Y$ , each elementary abelian of order $2^{n}$ , such that $H$ is generated by $X \cup Y$ , and $H/H'\cong X\tim…

math.CO2022

A characterisation of edge-affine $2$ -arc-transitive covers of $\K_{2^n,2^n}$

Daniel R. Hawtin, Cheryl E. Praeger, Jin-Xin Zhou

We introduce the notion of an \emph{ $n$ -dimensional mixed dihedral group}, a general class of groups for which we give a graph theoretic characterisation. In particular, if $H$ is…

math.CO2022

Finite $3$ -connected-set-homogeneous locally $2\K_n$ graphs and $s$ -arc-transitive graphs

Jinxin Zhou

In this paper, all graphs are assumed to be finite. For $s \geq 1$ and a graph $\G$, if for every pair of isomorphic connected induced subgraphs on at most $s$ vertices there exists…

math.CO2022

Two-geodesic transitive graphs of order $p^{n}$ with $n \leq 3$

Jun-Jie Huang, Yan-Quan Feng, Jin-Xin Zhou +1

A vertex triple $(u, v, w)$ of a graph is called a $2$ -geodesic if $v$ is adjacent to both $u$ and $w$ and $u$ is not adjacent to $w$ . A graph is said to be $2$ -geodesic transitive i…

math.CO2021★ 1 cited

On primitive $2$ -closed permutation groups of rank at most four

Michael Giudici, Luke Morgan, Jin-Xin Zhou

We characterise the primitive 2-closed groups $G$ of rank at most four that are not the automorphism group of a graph or digraph and show that if the degree is at least 2402 then t…

math.CO2021

Prime-valent Symmetric graphs with a quasi-semiregular automorphism

Fu-Gang Yin, Yan-Quan Feng, Jin-Xin Zhou +1

An automorphism of a graph is called quasi-semiregular if it fixes a unique vertex of the graph and its remaining cycles have the same length. This kind of symmetry of graphs was f…

math.CO2021

Normal Cayley digraphs of dihedral groups with CI-property

Jin-Hua Xie, Yan-Quan Feng, Jin-Xin Zhou

A Cayley (di)graph $C a y (G, S)$ of a group $G$ with respect to $S$ is said to be normal if the right regular representation of $G$ is normal in the automorphism group of $C a y (G, S)$ ,…

math.CO2021

Two-distance transitive normal Cayley graphs

Jun-Jie Huang, Yan-Quan Feng, Jin-Xin Zhou

In this paper, we construct an infinite family of normal Cayley graphs, which are $2$ -distance-transitive but neither distance-transitive nor $2$ -arc-transitive. This answers a que…

math.CO2020★ 4 cited

Stability of pair graphs

Yan-Li Qin, Binzhou Xia, Jin-Xin Zhou +1

We start up the study of the stability of general graph pairs. This notion is a generalization of the concept of the stability of graphs. We say that a pair of graphs $(Γ, Σ)$ is st…

math.CO2020★ 1 cited

Arc-transitive Cayley graphs on nonabelian simple groups with prime valency

Fu-Gang Yin, Yan-Quan Feng, Jin-Xin Zhou +1

In 2011, Fang et al. in (J. Combin. Theory A 118 (2011) 1039-1051) posed the following problem: Classify non-normal locally primitive Cayley graphs of finite simple groups of valen…

math.CO2019

Trivalent dihedrants and bi-dihedrants

Mi-Mi Zhang, Jin-Xin Zhou

A Cayley (resp. bi-Cayley) graph on a dihedral group is called a {\em dihedrant} (resp. {\em bi-dihedrant}). In 2000, a classification of trivalent arc-transitive dihedrants was gi…

math.CO2018★ 1 cited

Finite $3$ -connected homogeneous graphs

Cai Heng Li, Jin-Xin Zhou

A finite graph $\G$ is said to be {\em $(G, 3)$ - $($ connected $)$ homogeneous} if every isomorphism between any two isomorphic (connected) subgraphs of order at most $3$ extends to an…

Enumeration of orientably-regular maps with automorphism group $\PGam(2,2^p)$ for prime p

A transfer principle for Steklov eigenvalue estimates of graphs

The finite k-set homogeneous graphs

On automorphism groups of half-arc-transitive tetravalent graphs

Eigenvalue bounds for combinatorial Laplacians and an application to random complexes

On tetravalent half-arc-transitive graphs

On kernel isomorphisms of m-Cayley digraphs and finite 2PCI-groups

Normal and non-normal Cayley digraphs on cyclic and dihedral groups

On isomorphisms of m-Cayley digraphs

The classification of two-distance transitive dihedrants

Quasiprimitive groups with a biregular dihedral subgroup,and arc-transitive bidihedrants

Using mixed dihedral groups to construct normal Cayley graphs, and a new bipartite 2-arc-transitive graph which is not a Cayley graph

A family of 2-groups and an associated family of semisymmetric, locally 2-arc-transitive graphs

A characterisation of edge-affine 2-arc-transitive covers of $\K_{2^n,2^n}$

Finite 3-connected-set-homogeneous locally $2\K_n$ graphs and s-arc-transitive graphs

Two-geodesic transitive graphs of order pn with n≤3

On primitive 2-closed permutation groups of rank at most four

Prime-valent Symmetric graphs with a quasi-semiregular automorphism

Normal Cayley digraphs of dihedral groups with CI-property

Two-distance transitive normal Cayley graphs

Stability of pair graphs

Arc-transitive Cayley graphs on nonabelian simple groups with prime valency

Trivalent dihedrants and bi-dihedrants

Finite 3-connected homogeneous graphs

Enumeration of orientably-regular maps with automorphism group $\PGam(2,2^p)$ for prime $p$

The finite $k$ -set homogeneous graphs

On kernel isomorphisms of $m$ -Cayley digraphs and finite $2$ PCI-groups

On isomorphisms of $m$ -Cayley digraphs

Using mixed dihedral groups to construct normal Cayley graphs, and a new bipartite $2$ -arc-transitive graph which is not a Cayley graph

A family of $2$ -groups and an associated family of semisymmetric, locally $2$ -arc-transitive graphs

A characterisation of edge-affine $2$ -arc-transitive covers of $\K_{2^n,2^n}$

Finite $3$ -connected-set-homogeneous locally $2\K_n$ graphs and $s$ -arc-transitive graphs

Two-geodesic transitive graphs of order $p^{n}$ with $n \leq 3$

On primitive $2$ -closed permutation groups of rank at most four

Finite $3$ -connected homogeneous graphs