Shou-Jun Xu

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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.CO2023

Disproof of a conjecture on the edge Mostar index

Fazal Hayat, Shou-Jun Xu, Bo Zhou

For a given connected graph $G$ , the edge Mostar index $M o_{e} (G)$ is defined as $M o_{e} (G) = \sum_{e = uv \in E (G)} ∣ m_{u} (e ∣ G) - m_{v} (e ∣ G) ∣$ , where $m_{u} (e ∣ G)$ and $m_{v} (e ∣ G)$ are respectively…