Shengjie He

activity

20172023

most citedOn extremal cacti with respect to the edge Szeged index and edge-vertex Szeged index

3 citations · 5 across the 9 of their papers we have counts for

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9 papers · 1 filter

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 $c (G) = ∣ E (G) ∣ - ∣ V (G) ∣ + ω (G)$ …

math.CO2019★ 1 cited

Bounds for the rank of a complex unit gain graph in terms of the independence number

Shengjie He, Rong-Xia Hao, Aimei Yu

A complex unit gain graph (or $T$ -gain graph) is a triple $Φ = (G, T, φ)$ ( $(G, φ)$ for short) consisting of a graph $G$ as the underlying graph of $(G, φ)$ , $\math…

math.CO2019★ 1 cited

On the inertia index of a mixed graph with the matching number

Shengjie He, Rong-Xia Hao, Aimei Yu

A mixed graph $G$ is obtained by orienting some edges of $G$ , where $G$ is the underlying graph of $G$ . The positive inertia index, denoted by $p^{+} (G)$ , a…

math.CO2019

The rank of a complex unit gain graph in terms of the matching number

Shengjie He, Rong-Xia Hao, Fengming Dong

A complex unit gain graph (or $T$ -gain graph) is a triple $Φ = (G, T, φ)$ (or $(G, φ)$ for short) consisting of a simple graph $G$ , as the underlying graph of $(G…

math.CO2019

The relation between the independence number and rank of a signed graph

Shengjie He, Rong-Xia Hao

A signed graph $(G, σ)$ is a graph with a sign attached to each of its edges, where $G$ is the underlying graph of $(G, σ)$ . Let $c (G)$ , $α (G)$ and $r (G, σ)$ be the cyclomatic numb…

math.CO2018

Some useful lemmas on the edge Szeged index

Shengjie He

The edge Szeged index of a graph $G$ is defined as $S z_{e} (G) = uv \in E (G) \sum m_{u} (uv ∣ G) m_{v} (uv ∣ G)$ , where $m_{u} (uv ∣ G)$ (resp., $m_{v} (uv ∣ G)$ ) is the number of edges who…

math.CO2018

On extremal cacti with respect to the edge revised Szeged index

Shengjie He, Rong-Xia Hao, Deming Li

Let $G$ be a connected graph. The edge revised 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.CO2017★ 3 cited

On extremal cacti with respect to the edge Szeged index and edge-vertex Szeged index

Shengjie He, Rong-Xia Hao, Aimei Yu

The edge Szeged index and edge-vertex Szeged index of a graph are defined as $S z_{e} (G) = uv \in E (G) \sum m_{u} (uv ∣ G) m_{v} (uv ∣ G)$ and $Sz_{ev}(G)=\frac{1}{2} \sum\limits_{uv…

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

Bounds for the rank of a complex unit gain graph in terms of the independence number

On the inertia index of a mixed graph with the matching number

The rank of a complex unit gain graph in terms of the matching number

The relation between the independence number and rank of a signed graph

Some useful lemmas on the edge Szeged index

On extremal cacti with respect to the edge revised Szeged index

On extremal cacti with respect to the edge Szeged index and edge-vertex Szeged index

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