Muhuo Liu

activity

20182026

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

1 citations · 1 across the 11 of their papers we have counts for

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12 papers · 1 filter

math.CO2026

Spectral radius and edge-disjoint spanning trees of graphs with edge connectivity

Jia Wei, Muhuo Liu, Zhifu You +1

Let $τ (G)$ denote the maximum number of pairwise edge-disjoint spanning trees contained in a graph $G$ . Zhang and Fan [J. Graph Theory, 2026] posed the problem of determining the c…

math.CO2025

Decompositions of graphs with degree constraints relative to prescribed subgraphs

Peichao Wei, Muhuo Liu, Yang Wu +1

Given a finite simple undirected graph $G$ , let $T_{1} (G)$ denote the subset of vertices of $G$ such that every vertex of $T_{1} (G)$ belongs to at least one subgraph isomorphic to a gr…

math.CO2023

On the relationship between shortlex order and $A_{α}$ -spectral radii of graphs with starlike branch tree

Haiying Shan, Muhuo Liu

Let $P (n)$ denote the set of all partitions of $n$ , whose elements are nondecreasing sequences of positive integers whose sum is $n$ . For ${\bf a}=( n_{1}, n_{2},\ldots, n_{d}) \in…

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

Extremal problems on planar graphs without k edge-disjoint cycles

Zhai Mingqing, Liu Muhuo

In the 1960s, Erdős and his cooperators initiated the research of the maximum numbers of edges in a graph or a planar graph on $n$ vertices without $k$ edge-disjoint cycles. This p…

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.CO2021

A tight lower bound on the matching number of graphs via Laplacian eigenvalues

Xiaofeng Gu, Muhuo Liu

Let $α^{'}$ and $μ_{i}$ denote the matching number of a non-empty simple graph $G$ with $n$ vertices and the $i$ -th smallest eigenvalue of its Laplacian matrix, respectively. In this pa…

math.CO2020

Spectral strengthening of a theorem on transversal critical graphs

Muhuo Liu, Xiaofeng Gu

A transversal set of a graph $G$ is a set of vertices incident to all edges of $G$ . The transversal number of $G$ , denoted by $τ (G)$ , is the minimum cardinality of a transversal se…

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…

Spectral radius and edge-disjoint spanning trees of graphs with edge connectivity

Decompositions of graphs with degree constraints relative to prescribed subgraphs

On the relationship between shortlex order and Aα​-spectral radii of graphs with starlike branch tree

Note on Sombor index of connected graphs with given degree sequence

Extremal problems on planar graphs without k edge-disjoint cycles

A unified combinatorial view beyond some spectral properties

The k-apex trees with minimum augmented Zagreb index

A tight lower bound on the matching number of graphs via Laplacian eigenvalues

Spectral strengthening of a theorem on transversal critical graphs

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

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

Unified spectral hamiltonian results of balanced bipartite graphs and complementary graphs

On the relationship between shortlex order and $A_{α}$ -spectral radii of graphs with starlike branch tree

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

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