Hechao Liu

activity

20212023

most citedThe expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

36 citations · 50 across the 13 of their papers we have counts for

collaborators

14 papers

math.GM2023

Note on VDB Topological Indices of k-Cyclic Graphs

Hechao Liu, Zenan Du, Yufei Huang +2

Let $G$ be a connected graph with $n$ vertices and $m$ edges. The vertex-degree-based topological index (VDB) (or graphical function-index) $T I (G)$ of $G$ with edge-weight function…

math.CO2022★ 2 cited

Extremal Kirchhoff index in polycyclic chains

Hechao Liu, Lihua You

The Kirchhoff index of graphs, introduced by Klein and Randić in 1993, has been known useful in the study of computer science, complex network and quantum chemistry. The Kirchhoff…

math.CO2022

Proof of an open problem on the Sombor index

Hechao Liu

The Sombor index is one of the geometry-based descriptors, which was defined as $S O (G) = uv \in E (G) \sum d^{2} (u) + d^{2} (v),$ where $d (u)$ (resp. $d (v)$ ) denotes the degree…

math.CO2022★ 5 cited

Mathematical and chemistry properties of geometry-based invariants

Hechao Liu

Recently, based on elementary geometry, Gutman proposed several geometry-based invariants (i.e., $S O$ , $S O_{1}$ , $S O_{2}$ , $S O_{3}$ , $S O_{4}$ , $S O_{5}$ , $S O_{6}$ ). The Sombor index…

math.CO2022

The spread of generalized reciprocal distance matrix

Hechao Liu, Yufei Huang

The generalized reciprocal distance matrix $R D_{α} (G)$ was defined as $R D_{α} (G) = α R T (G) + (1 - α) R D (G), 0 \leq α \leq 1.$ Let $λ_{1}(RD_α(G))\geq λ_{2}(RD_α(G))\geq \cdots \geq λ_{n}(RD…

math.CO2022★ 1 cited

Sharp bounds on the symmetric division deg index of graphs and line graphs

Hechao Liu, Yufei Huang

For a graph $G$ with vertex set $V_{G}$ and edge set $E_{G}$ , the symmetric division deg index is defined as $SDD(G)=\sum\limits_{uv\in E_{G}}(\frac{d_{u}}{d_{v}}+\frac{d_{v}}{d_{u…

math.GM2022

Maximum zeroth-order general Randić index of orientations of cacti

Jiaxiang Yang, Hanyuan Deng, Zikai Tang +1

The zeroth-order general Randić index $R_{a + 1}^{0}$ of an $n$ -vertices oriented graph $D$ is equal to the sum of $(d_{u_{i}}^{+})^{a} + (d_{u_{j}}^{-})^{a}$ over all arcs $u_{i} u_{j}$ of $D$ …

math.CO2022

The Sombor index and coindex of two-trees

Zenan Du, Lihua You, Hechao Liu +1

The Sombor index of a graph $G$ , introduced by Ivan Gutman, is defined as the sum of the weights $d_{G} (u)^{2} + d_{G} (v)^{2}$ of all edges $uv$ of $G$ , where $d_{G} (u)$ denotes the deg…

math.CO2021

Extremal problems on Sombor indices of unicyclic graphs with a given diameter

Hechao Liu

Sombor index is a novel topological index, which was introduced by Gutman and defined for a graph $G$ as $S O (G) = uv \in E (G) \sum d_{u}^{2} + d_{v}^{2}$ , where $d_{u}=d_…

math.CO2021★ 2 cited

Spectral properties of $p$ -Sombor matrices and beyond

Hechao Liu, Lihua You, Yufei Huang +1

Let $G = (V (G), E (G))$ be a simple graph with vertex set $V (G) = {v_{1}, v_{2}, \dots, v_{n}}$ and edge set $E (G)$ . The $p$ -Sombor matrix $S_{p} (G)$ of $G$ is the square matr…

math.CO2021

Extremal cacti with respect to Sombor index

Hechao Liu

Recently, a novel topological index, Sombor index, was introduced by Gutman, defined as $S O (G) = uv \in E (G) \sum d_{u}^{2} + d_{v}^{2}$ , where $d_{u}$ denotes the degree…

math.CO2021★ 36 cited

The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

Xiaona Fang, Lihua You, Hechao Liu

Hexagonal chains are a special class of catacondensed benzenoid system and phenylene chains are a class of polycyclic aromatic compounds. Recently, A family of Sombor indices was i…

math.CO2021★ 2 cited

Ordering chemical graphs by Sombor indices and its applications

Hechao Liu, Lihua You, Yufei Huang

Topological indices are a class of numerical invariants that predict certain physical and chemical properties of molecules. Recently, two novel topological indices, named as Sombor…

math.CO2021★ 2 cited

On the first three minimum Mostar indices of tree-like phenylenes

Hechao Liu, Lihua You, Hanlin Chen +1

Let $G = (V_{G}, E_{G})$ be a simple connected graph with its vertex set $V_{G}$ and edge set $E_{G}$ . The Mostar index $M o (G)$ was defined as $Mo(G)=\sum\limits_{e=uv\in E(G)}|n_{u…

Note on VDB Topological Indices of k-Cyclic Graphs

Extremal Kirchhoff index in polycyclic chains

Proof of an open problem on the Sombor index

Mathematical and chemistry properties of geometry-based invariants

The spread of generalized reciprocal distance matrix

Sharp bounds on the symmetric division deg index of graphs and line graphs

Maximum zeroth-order general Randić index of orientations of cacti

The Sombor index and coindex of two-trees

Extremal problems on Sombor indices of unicyclic graphs with a given diameter

Spectral properties of p-Sombor matrices and beyond

Extremal cacti with respect to Sombor index

The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

Ordering chemical graphs by Sombor indices and its applications

On the first three minimum Mostar indices of tree-like phenylenes

Spectral properties of $p$ -Sombor matrices and beyond