Shengjie He

collaborators

2 papers

math.CO2023

The extremal unicyclic graphs of the revised edge Szeged index with given diameter

Shengjie He, Qiaozhi Geng, Rong-Xia Hao

Let $G$ be a connected graph. The revised edge Szeged index of $G$ is defined as $Sz^{\ast}_{e}(G)=\sum\limits_{e=uv\in E(G)}(m_{u}(e|G)+\frac{m_{0}(e|G)}{2})(m_{v}(e|G)+\frac{m_{0…

math.CO2023

No mixed graph with the nullity $η (G) = ∣ V (G) ∣ - 2 m (G) + 2 c (G) - 1$

Shengjie He, Rong-Xia Hao, Hong-Jian Lai +1

A mixed graph $G$ is obtained from a simple undirected graph $G$ , the underlying graph of $G$ , by orienting some edges of $G$ . Let $c (G) = ∣ E (G) ∣ - ∣ V (G) ∣ + ω (G)$ …

The extremal unicyclic graphs of the revised edge Szeged index with given diameter

No mixed graph with the nullity η(G)=∣V(G)∣−2m(G)+2c(G)−1

No mixed graph with the nullity $η (G) = ∣ V (G) ∣ - 2 m (G) + 2 c (G) - 1$