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Yuefeng Yang

Publications and source records attributed to Yuefeng Yang.

At least 19 recordsLinked to original sources
arXiv2026

Two-disjoint-cycle-cover vertex pancyclicity of split-star networks

Let $r_1$ and $r_2$ be positive integers with $r_1 \le r_2$. A graph $G$ is called $2$-DCC vertex $[r_1,r_2]$-pancyclic if, for any two distinct vertices of $G$ and any integer $\ell \in [r_1,r_2]$, there exist two vertex-disjoint cycles of lengths $\ell$ and $|V(G)|-\ell$, respectively, containing the two vertices separately. In this paper, we investigate the two-disjoint-cycle-cover vertex pancyclicity of the split-star network $S_n^2$. We prove that $S_n^2$ is $2$-DCC vertex $[3,n!/2]$-pancyclic for $n\ge4$.

math.CO↗
arXiv2025

Regular sets in Cayley sum graphs on generalized dicyclic groups

For a graph $\Gamma=(V(\Gamma),E(\Gamma))$, a subset $C$ of $V(\Gamma)$ is called an $(\alpha,\beta)$-regular set in $\Gamma$, if every vertex of $C$ is adjacent to exactly $\alpha$ vertices of $C$ and every vertex of $V(\Gamma)\setminus C$ is adjacent to exactly $\beta$ vertices of $C$. In particular, if $C$ is an $(\alpha,\beta)$-regular set in some Cayley sum graph of a finite group $G$ with connection set $S$, then $C$ is called an $(\alpha,\beta)$-regular set of $G$. In this paper, we consider a generalized dicyclic group $G$ and for each subgroup $H$ of $G$, by giving an appropriate connection set $S$, we determine each possibility for $(\alpha,\beta)$ such that $H$ is an $(\alpha,\beta)$-regular set of $G$.

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arXiv2025

Perfect codes in quartic Cayley graphs of generalized dihedral groups

For a graph $\Gamma=(V\Gamma,E\Gamma)$, a subset $D$ of $V\Gamma$ is a perfect code in $\Gamma$ if every vertex of $\Gamma$ is dominated by exactly one vertex in $D$. In this paper, we classify all connected quartic Cayley graphs on generalized dihedral groups admitting a perfect code, and determine all perfect codes in such graphs.

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arXiv2025

Semicomplete multipartite weakly distance-regular digraphs

A digraph is semicomplete multipartite if its underlying graph is a complete multipartite graph. As a special case of semicomplete multipartite digraphs, J{\o}rgensen et al. \cite{JG14} initiated the study of doubly regular team tournaments. As a natural extension, we introduce doubly regular team semicomplete multipartite digraphs and show that such digraphs fall into three types. Furthermore, we give a characterization of all semicomplete multipartite commutative weakly distance-regular digraphs.

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arXiv2024

(Total) Perfect codes in (extended) subgroup sum graphs

Given a finite group $G$ with identity $e$ and a normal subgroup $H$ of $G$, the subgroup sum graph $\Gamma_{G,H}$ (resp. extended subgroup sum graph $\Gamma_{G,H}^+$) of $G$ with respect to $H$ is the graph with vertex set $G$, in which distinct vertices $x$ and $y$ are adjacent whenever $xy\in H\setminus \{e\}$ (resp. $xy\in H$). A group $G$ is said to be {\em code-perfect} if for any normal subgroup $H$ of $G$, $\Gamma_{G,H}$ admits a perfect code. In this paper, we give a necessary and sufficient condition for which normal subgroups $H$ of $G$ satisfy that a (extended) subgroup sum graph of $G$ with respect to $H$ admits a (total) perfect code, and classify all code-perfect Dedekind groups. As an application, we classify all normal subgroups such that the subgroup sum graph of a cyclic group, a dihedral group or a dicyclic group with respect to such a normal subgroup admits perfect codes, respectively. We also determine all abelian groups $A$ and subgroups $H$ of $A$ such that $\Gamma_{A,H}$ admits a total perfect code.

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arXiv2024

Every nonsymmetric $4$-class association scheme can be generated by a digraph

A (di)graph $\Gamma$ generates a commutative association scheme $\mathfrak{X}$ if and only if the adjacency matrix of $\Gamma$ generates the Bose-Mesner algebra of $\mathfrak{X}$. In [17, Theorem 1.1], Monzillo and Penji\'{c} proved that, except for amorphic symmetric association schemes, every $3$-class association scheme can be generated by the adjacency matrix of a (di)graph. In this paper, we characterize when a commutative association scheme with exactly one pair of nonsymmetric relations can be generated by a digraph under certain assumptions. As an application, we show that each nonsymmetric $4$-class association scheme can be generated by a digraph.

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arXiv2024

Weakly distance-regular digraphs whose underlying graphs are distance-regular,II

Weakly distance-regular digraphs are a natural directed version of distance-regular graphs. In [16], we classified all commutative weakly distance-regular digraphs whose underlying graphs are Hamming graphs, folded n-cubes, or Doob graphs. In this paper, we classify all commutative weakly distance-regular digraphs whose underlying graphs are Johnson graphs or folded Johnson graphs.

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arXiv2024

Locally semicomplete weakly distance-regular digraphs

A digraph is semicomplete if any two vertices are connected by at least one arc and is locally semicomplete if the out-neighbourhood (resp. in-neighbourhood) of any vertex induces a semicomplete digraph. In this paper, we characterize all locally semicomplete weakly distance-regular digraphs under the assumption of commutativity.

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arXiv2023

Perfect codes in 2-valent Cayley digraphs on abelian groups

For a digraph $\Gamma$, a subset $C$ of $V(\Gamma)$ is a perfect code if $C$ is a dominating set such that every vertex of $\Gamma$ is dominated by exactly one vertex in $C$. In this paper, we classify strongly connected 2-valent Cayley digraphs on abelian groups admitting a perfect code, and determine completely all perfect codes of such digraphs.

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arXiv2023

Weakly distance-regular circulants, I

We classify certain non-symmetric commutative association schemes. As an application, we determine all the weakly distance-regular circulants of one type of arcs by using Schur rings. We also give the classification of primitive weakly distance-regular circulants.

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arXiv2023

Weakly distance-regular digraphs whose underlying graphs are distance-regular, I

Weakly distance-regular digraphs are a natural directed version of distance-regular graphs. In [8], the third author and Suzuki proposed a question when an orientation of a distance-regular graph defines a weakly distance-regular digraph. In this paper, we initiate this project, and classify all commutative weakly distance-regular digraphs whose underlying graphs are Hamming graphs, folded n-cubes and Doob graphs, respectively.

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arXiv2022

Perfect codes in quintic Cayley graphs on abelian groups

A subset $C$ of the vertex set of a graph $\Gamma$ is called a perfect code of $\Gamma$ if every vertex of $\Gamma$ is at distance no more than one to exactly one vertex in $C$. In this paper, we classify all connected quintic Cayley graphs on abelian groups that admit a perfect code, and determine completely all perfect codes of such graphs.

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arXiv2021

Weakly distance-regular digraphs of one type of arcs

In this paper, we classify all commutative weakly distance-regular digraphs of girth $g$ and one type of arcs under the assumption that $p_{(1,g-1),(1,g-1)}^{(2,g-2)}\geq k_{1,g-1}-2$. In consequence, we recover [13, Theorem 1.1] as a special case of our result.

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arXiv2020

On weak metric dimension of digraphs

Using the two way distance, we introduce the concepts of weak metric dimension of a strongly connected digraph $Γ$. We first establish lower and upper bounds for the number of arcs in $Γ$ by using the diameter and weak metric dimension of $Γ$, and characterize all digraphs attaining the lower or upper bound. Then we study a digraph with weak metric dimension $1$ and classify all vertex-transitive digraphs having weak metric dimension $1$. Finally, all digraphs of order $n$ with weak metric dimension $n-1$ or $n-2$ are determined.

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arXiv2020

Perfect codes in Cayley sum graphs

A subset $C$ of the vertex set of a graph $Γ$ is called a perfect code of $Γ$ if every vertex of $Γ$ is at distance no more than one to exactly one vertex in $C$. Let $A$ be a finite abelian group and $T$ a square-free subset of $A$. The Cayley sum graph of $A$ with respect to the connection set $T$ is a simple graph with $A$ as its vertex set, and two vertices $x$ and $y$ are adjacent whenever $x+y\in T$. A subgroup of $A$ is said to be a subgroup perfect code of $A$ if the subgroup is a perfect code of some Cayley sum graph of $A$. In this paper, we give some necessary and sufficient conditions for a subset of $A$ to be a perfect code of a given Cayley sum graph of $A$. We also characterize all subgroup perfect codes of $A$.

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