arXiv subjects

Ruichao Niu

Publications and source records attributed to Ruichao Niu.

3 recordsLinked to original sources

arXiv2026

Two-disjoint-cycle-cover edge bipancyclicity of bipartite generalized hypercubes

Let $G=C(d_1,\ldots,d_n)=F_1\BoxProd\cdots\BoxProd F_n$ be a bipartite generalized hypercube with $n\geq2$, all $d_i$ even, and $N=|V(G)|\geq8$, where $F_i=K_2$ when $d_i=2$, and $F_i=C_{d_i}$ when $d_i\geq4$. We prove the following exact strengthening of two-disjoint-cycle-cover vertex bipancyclicity. For every ordered pair of independent edges $e,f\in E(G)$ and every even integer $4\leq\ell\leq N-4$, the vertex set can be partitioned into two cycles $J_1,J_2$ of lengths $\ell$ and $N-\ell$, respectively, with $e\in E(J_1)$ and $f\in E(J_2)$, if and only if $G$ is not isomorphic to any $K_2\BoxProd C_{2p}$ with $p\geq3$. The graph $C(2,2)\cong C_4$ is treated separately: it has no 2-DCC. Consequences that retain prescribed-edge information include ordinary edge bipancyclicity and the even $k$-ary $n$-cube specialization.

math.CO↗

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

Neighbor Connectivity of Undirected Toroidal Meshes

In this paper, we examine the neighbor connectivity, denoted as $κ_{NB}$, of the undirected toroidal mesh $C(d_1,d_2,\ldots,d_n)$. We demonstrate that $κ_{NB}(C(d_1,d_2,\ldots,d_n)) = n$ for all $n \ge 2$ and $d_i \ge 3$ (for $1 \le i \le n$). Additionally, we perform a computer simulation experiment on neighbor connectivity in undirected toroidal meshes. This experiment not only supports our theoretical findings with empirical results but also provides a deeper understanding of neighbor structure failures in undirected toroidal meshes.

math.CO↗