Shou‐Jun Xu

collaborators

3 papers

math.CO2024

Ultra log-concavity and real-rootedness of dependence polynomials

Yan-Ting Xie, Shou-Jun Xu

For some positive integer $m$ , a real polynomial $P (x) = k = 0 \sum m a_{k} x^{k}$ with $a_{k} ⩾ 0$ is called log-concave (resp. ultra log-concave) if $a_k^2\geqslant a_{k-1}a_…

math.CO2024

Solution to a conjecture on resistance distances of block tower graphs

Wensheng Sun, Yujun Yang, Wuxian Chen +1

Let $G$ be a connected graph. The resistance distance between two vertices $u$ and $v$ of $G$ , denoted by $R_{G} [u, v]$ , is defined as the net effective resistance between them in t…

math.CO2024

Perfect codes in circulant graphs of degree $p^{l} - 1$

Xiaomeng Wang, Oriol Serra, Shou-Jun Xu +1

A perfect code in a graph is an independent set of the graph such that every vertex outside the set is adjacent to exactly one vertex in the set. A circulant graph is a Cayley grap…

Ultra log-concavity and real-rootedness of dependence polynomials

Solution to a conjecture on resistance distances of block tower graphs

Perfect codes in circulant graphs of degree pl−1

Perfect codes in circulant graphs of degree $p^{l} - 1$