Muhuo Liu

activity

20182022

most citedNote on Sombor index of connected graphs with given degree sequence

1 citations · 1 across the 3 of their papers we have counts for

collaborators

6 papers

math.CO2022★ 1 cited

Note on Sombor index of connected graphs with given degree sequence

Peichao Wei, Muhuo Liu

For a simple connected graph $G = (V, E)$ , let $d (u)$ be the degree of the vertex $u$ of $G$ . The general Sombor index of $G$ is defined as $$SO_α(G)=\sum_{uv\in E} \left[d(u)^2+d(v)^…

math.CO2022

A unified combinatorial view beyond some spectral properties

Xiaofeng Gu, Muhuo Liu

Let $β > 0$ . Motivated by jumbled graphs defined by Thomason, the celebrated expander mixing lemma and Haemers's vertex separation inequality, we define that a graph $G$ with $n$ ver…

math.CO2022

The $k$ -apex trees with minimum augmented Zagreb index

Muhuo Liu, Shumei Pang, Francesco Belardo +1

For a connected graph $G$ on at least three vertices, the augmented Zagreb index (AZI) of $G$ is defined as $$AZI(G)=\sum_{uv\in E(G)}\left(\frac{d(u)d(v)}{d(u)+d(v)-2}\right)^{3},…

math.CO2019

The general spectral radius and majorization theorem of $t$ -cone graphs with given degree sequences

Yufei Huang, Muhuo Liu

The general spectral radius of a graph $G$ , denoted by $Θ (G, α)$ , is the maximal eigenvalue of $M_{α} (G) = A (G) + α D (G)$ $(α \geq 0)$ , where $A (G)$ and $D (G)$ are the adjacency matrix and…

math.CO2018

Extremal graphs for vertex-degree-based invariants with given degree sequences

Muhuo Liu, Kexiang Xu, Xiao-Dong Zhang

For a symmetric bivariable function $f (x, y)$ , let the {\it connectivity function} of a connected graph $G$ be $M_{f} (G) = \sum_{uv \in E (G)} f (d (u), d (v))$ , where $d (u)$ is the degree of…

math.CO2018

Unified spectral hamiltonian results of balanced bipartite graphs and complementary graphs

Muhuo Liu, Yang Wu, Hong-Jian Lai

There have been researches on sufficient spectral conditions for Hamiltonian properties and path-coverable properties of graphs. Utilizing the Bondy-Chvátal closure, we provide a u…