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

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Showing 2022Show all

7 papers · 1 filter

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…