Sanming Zhou
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Sanming Zhou has a total of 125 co-authors. Here are the top co-authors by number of shared publications:
- Binzhou Xia
School of Mathematics and Statistics, The University of Melbourne, Parkville, Australia
18 shared publications - Xiaogang Liu
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, P. R. China
9 shared publications Alison Thomson
Department of Mathematics Statistics The University of Melbourne 3010 Parkville VIC Australia
5 shared publications- Cheryl E. Praeger
The University of Western Australia
5 shared publications - Devsi Bantva
Department of Mathematics Lukhdhirji Engineering College 363 642 Morvi Gujarat India
5 shared publications - Hamid Mokhtar
School of Mathematics and Statistics The University of Melbourne 3010 Parkville VIC Australia
5 shared publications
Latest Publications
- Open Access
- 9 April 2026
- Published by Springer Nature in Designs, Codes and Cryptography
- Vol. 94 (4) , 87
Perfect codes in Cayley graphs of abelian groups
A perfect code in a graph $$\Gamma = (V, E)$$ is a subset C of V such that no two vertices in C are adjacent and every vertex in $$V \setminus C$$ is adjacent to exactly one vertex in C . A total perfect code in $$\Gamma $$ is a subset C of V such that every vertex of $$\Gamma $$ is adjacent to exactly one vertex in C . In this paper we prove several results on perfect codes and total perfect codes in Cayley graphs of finite abelian groups.- 9 April 2026
- Published by Springer Nature in Designs, Codes and Cryptography
- Vol. 94 (4) , 87
Open AccessPerfect codes in Cayley graphs of abelian groups
A perfect code in a graph $$\Gamma = (V, E)$$ is a subset C of V such that no two vertices in C are adjacent and every vertex in $$V \setminus C$$ is adjacent to exactly one vertex in C . A total perfect code in $$\Gamma $$ is a subset C of V such that every vertex of $$\Gamma $$ is adjacent to exactly one vertex in C . In this paper we prove several results on perfect codes and total perfect codes in Cayley graphs of finite abelian groups. - Open Access
Perfect codes in Cayley graphs of Hajós groups
A perfect code in a graph $Γ$ is a subset $C$ of the vertex set of $Γ$ such that every vertex of $Γ$ outside $C$ has exactly one neighbour in $C$. A perfect code in a directed graph can be defined similarly by requiring that for every vertex $v$ outside $C$ there exists exactly one vertex $u$ in $C$ such that the arc from $u$ to $v$ exists in $Γ$. A subset $X$ of an abelian group $G$ is said to be periodic if there exists a non-identity element $g$ of $G$ such that $g + X = X$. A factorization of $G$ is a pair of nonempty subsets $(A, B)$ of $G$ such that every element $g$ of $G$ can be expressed uniquely as $g = a+b$ with $a \in A$ and $b \in B$. If for every factorization $(A, B)$ of an abelian group $G$ at least one of $A$ and $B$ is periodic, then $G$ is said to be a Hajós group. In this paper we classify all Cayley graphs (directed or undirected) of Hajós groups which admit perfect codes, and moreover we determine all perfect codes in such Cayley graphs.Open AccessPerfect codes in Cayley graphs of Hajós groups
A perfect code in a graph $Γ$ is a subset $C$ of the vertex set of $Γ$ such that every vertex of $Γ$ outside $C$ has exactly one neighbour in $C$. A perfect code in a directed graph can be defined similarly by requiring that for every vertex $v$ outside $C$ there exists exactly one vertex $u$ in $C$ such that the arc from $u$ to $v$ exists in $Γ$. A subset $X$ of an abelian group $G$ is said to be periodic if there exists a non-identity element $g$ of $G$ such that $g + X = X$. A factorization of $G$ is a pair of nonempty subsets $(A, B)$ of $G$ such that every element $g$ of $G$ can be expressed uniquely as $g = a+b$ with $a \in A$ and $b \in B$. If for every factorization $(A, B)$ of an abelian group $G$ at least one of $A$ and $B$ is periodic, then $G$ is said to be a Hajós group. In this paper we classify all Cayley graphs (directed or undirected) of Hajós groups which admit perfect codes, and moreover we determine all perfect codes in such Cayley graphs. - Open Access
Which maximal subgroups are perfect codes?
A perfect code in a graph $Γ=(V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. A subgroup $H$ of a group $G$ is called a subgroup perfect code of $G$ if it is a perfect code in some Cayley graph of $G$. In this paper, we undertake a systematic study of which maximal subgroups of a group can be perfect codes. Our approach highlights a characterization of subgroup perfect codes in terms of their ``local'' complements.Open AccessWhich maximal subgroups are perfect codes?
A perfect code in a graph $Γ=(V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. A subgroup $H$ of a group $G$ is called a subgroup perfect code of $G$ if it is a perfect code in some Cayley graph of $G$. In this paper, we undertake a systematic study of which maximal subgroups of a group can be perfect codes. Our approach highlights a characterization of subgroup perfect codes in terms of their ``local'' complements. - Open Access
Perfect codes in Cayley graphs of abelian groups
A perfect code in a graph $Γ= (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. A total perfect code in $Γ$ is a subset $C$ of $V$ such that every vertex of $Γ$ is adjacent to exactly one vertex in $C$. In this paper we prove several results on perfect codes and total perfect codes in Cayley graphs of finite abelian groups.Open AccessPerfect codes in Cayley graphs of abelian groups
A perfect code in a graph $Γ= (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. A total perfect code in $Γ$ is a subset $C$ of $V$ such that every vertex of $Γ$ is adjacent to exactly one vertex in $C$. In this paper we prove several results on perfect codes and total perfect codes in Cayley graphs of finite abelian groups. - Open Access
Odd Hadwiger's conjecture for the complements of Kneser graphs
A generalization of the four-color theorem, Hadwiger's conjecture is considered as one of the most important and challenging problems in graph theory, and odd Hadwiger's conjecture is a strengthening of Hadwiger's conjecture by way of signed graphs. In this paper, we prove that odd Hadwiger's conjecture is true for the complements K(n, k) of the Kneser graphs K(n, k), where n ≥ 2k ≥ 4. This improves a result of G. Xu and S. Zhou (2017) which states that Hadwiger's conjecture is true for this family of graphs. Moreover, we prove that K(n, k) contains a 1-shallow complete minor of a special type with order no less than the chromatic number χ(K(n, k)), and in the case when 7 ≤ 2k + 1 ≤ n ≤ 3k -1 the gap between the odd Hadwiger number and chromatic number of K(n, k) is Ω(1.5 k ).
Open AccessOdd Hadwiger's conjecture for the complements of Kneser graphs
A generalization of the four-color theorem, Hadwiger's conjecture is considered as one of the most important and challenging problems in graph theory, and odd Hadwiger's conjecture is a strengthening of Hadwiger's conjecture by way of signed graphs. In this paper, we prove that odd Hadwiger's conjecture is true for the complements K(n, k) of the Kneser graphs K(n, k), where n ≥ 2k ≥ 4. This improves a result of G. Xu and S. Zhou (2017) which states that Hadwiger's conjecture is true for this family of graphs. Moreover, we prove that K(n, k) contains a 1-shallow complete minor of a special type with order no less than the chromatic number χ(K(n, k)), and in the case when 7 ≤ 2k + 1 ≤ n ≤ 3k -1 the gap between the odd Hadwiger number and chromatic number of K(n, k) is Ω(1.5 k ).
- Open Access
Odd Hadwiger's conjecture for the complements of Kneser graphs
A generalization of the four-color theorem, Hadwiger's conjecture is considered as one of the most important and challenging problems in graph theory, and odd Hadwiger's conjecture is a strengthening of Hadwiger's conjecture by way of signed graphs. In this paper, we prove that odd Hadwiger's conjecture is true for the complements $\overline{K}(n,k)$ of the Kneser graphs $K(n,k)$, where $n\geq 2k \ge 4$. This improves a result of G. Xu and S. Zhou (2017) which states that Hadwiger's conjecture is true for this family of graphs. Moreover, we prove that $\overline{K}(n,k)$ contains a 1-shallow complete minor of a special type with order no less than the chromatic number $χ(\overline{K}(n,k))$, and in the case when $7 \le 2k+1 \le n \le 3k-1$ the gap between the odd Hadwiger number and chromatic number of $\overline{K}(n,k)$ is $Ω(1.5^{k})$.Open AccessOdd Hadwiger's conjecture for the complements of Kneser graphs
A generalization of the four-color theorem, Hadwiger's conjecture is considered as one of the most important and challenging problems in graph theory, and odd Hadwiger's conjecture is a strengthening of Hadwiger's conjecture by way of signed graphs. In this paper, we prove that odd Hadwiger's conjecture is true for the complements $\overline{K}(n,k)$ of the Kneser graphs $K(n,k)$, where $n\geq 2k \ge 4$. This improves a result of G. Xu and S. Zhou (2017) which states that Hadwiger's conjecture is true for this family of graphs. Moreover, we prove that $\overline{K}(n,k)$ contains a 1-shallow complete minor of a special type with order no less than the chromatic number $χ(\overline{K}(n,k))$, and in the case when $7 \le 2k+1 \le n \le 3k-1$ the gap between the odd Hadwiger number and chromatic number of $\overline{K}(n,k)$ is $Ω(1.5^{k})$. - 21 March 2025
- Published by Springer Nature in Graphs and Combinatorics
- Vol. 41 (2) , 1-22
Stability of Graph Pairs Involving Cycles
- 21 March 2025
- Published by Springer Nature in Graphs and Combinatorics
- Vol. 41 (2) , 1-22
Stability of Graph Pairs Involving Cycles
- Open Access
Determining the vertex stabilizers of 4-valent half-arc-transitive graphs
We say that a group is a $4$-HAT-stabilizer if it is the vertex stabilizer of some connected $4$-valent half-arc-transitive graph. In 2001, Marušič and Nedela proved that every $4$-HAT-stabilizer must be a concentric group. However, over the past two decades, only a very small proportion of concentric groups have been shown to be $4$-HAT-stabilizers. This paper develops a theory that provides a general framework for determining whether a concentric group is a $4$-HAT-stabilizer. With this approach, we significantly extend the known list of $4$-HAT-stabilizers. As a corollary, we confirm that $\mathcal{H}_7\times C_2^{m-7}$ are $4$-HAT-stabilizers for $m\geq 7$, achieving the goal of a conjecture posed by Spiga and Xia.Open AccessDetermining the vertex stabilizers of 4-valent half-arc-transitive graphs
We say that a group is a $4$-HAT-stabilizer if it is the vertex stabilizer of some connected $4$-valent half-arc-transitive graph. In 2001, Marušič and Nedela proved that every $4$-HAT-stabilizer must be a concentric group. However, over the past two decades, only a very small proportion of concentric groups have been shown to be $4$-HAT-stabilizers. This paper develops a theory that provides a general framework for determining whether a concentric group is a $4$-HAT-stabilizer. With this approach, we significantly extend the known list of $4$-HAT-stabilizers. As a corollary, we confirm that $\mathcal{H}_7\times C_2^{m-7}$ are $4$-HAT-stabilizers for $m\geq 7$, achieving the goal of a conjecture posed by Spiga and Xia. - Open Access
- 11 January 2025
- Published by Combinatorial Press in Congressus Numerantium
- Vol. 235, 3-4
Congressus Numerantium: A new beginning
Congressus Numerantium (CN) is an esteemed international journal with a long history of publishing high-quality papers in combinatorics and related areas. Founded by the late Professor Ralph Gordon Stanton and with its first volume appeared in 1970, CN began with a series of conference proceedings in mathematics, but later it also published regular contributions directly submitted to the journal. In the past over 50 years, a large number of conferences published their proceedings in CN. Among them the first ones include: Southeastern Conference on Combinatorics, Graph Theory, and Computing; Louisiana Conference on Combinatorics, Graph Theory, and Computing; West Coast Conference on Combinatorics, Graph Theory, and Computing; Manitoba Conference on Numerical Mathematics and Computing; British Combinatorial Conference; Canadian Workshop on the Design and Development of Computer Systems; Conference on Algebraic Aspects of Combinatorics; International Conference on ALGOL 68 Implementation; Sundance Conference.
- 11 January 2025
- Published by Combinatorial Press in Congressus Numerantium
- Vol. 235, 3-4
Open AccessCongressus Numerantium: A new beginning
Congressus Numerantium (CN) is an esteemed international journal with a long history of publishing high-quality papers in combinatorics and related areas. Founded by the late Professor Ralph Gordon Stanton and with its first volume appeared in 1970, CN began with a series of conference proceedings in mathematics, but later it also published regular contributions directly submitted to the journal. In the past over 50 years, a large number of conferences published their proceedings in CN. Among them the first ones include: Southeastern Conference on Combinatorics, Graph Theory, and Computing; Louisiana Conference on Combinatorics, Graph Theory, and Computing; West Coast Conference on Combinatorics, Graph Theory, and Computing; Manitoba Conference on Numerical Mathematics and Computing; British Combinatorial Conference; Canadian Workshop on the Design and Development of Computer Systems; Conference on Algebraic Aspects of Combinatorics; International Conference on ALGOL 68 Implementation; Sundance Conference.
- 29 November 2024
- Published by Springer Nature in Journal of Algebraic Combinatorics
- Vol. 61 (1) , 1-20
A family of symmetric graphs in relation to 2-point-transitive linear spaces
- 29 November 2024
- Published by Springer Nature in Journal of Algebraic Combinatorics
- Vol. 61 (1) , 1-20
A family of symmetric graphs in relation to 2-point-transitive linear spaces