Shengjie He

activity

20172019

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

3 citations · 3 across the 2 of their papers we have counts for

collaborators

7 papers

math.CO2019

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

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…