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The Spectral Properties of p-Sombor(Laplacian)Matrix of Graphs

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Journal of Mathematical Research with Applications 2023年第3期43卷 277-288页

作者： Hechao LIU lihua you School of Mathematical Sciences South China Normal University

The Sombor index,which was recently introduced into chemical graph theory,can predict physico-chemical properties of molecules.In this paper,we investigate the properties of (p-)Sombor index from an algebraic viewpoint.The p-Sombor matrix Sp(G) is the square matrix of order n whose (i,j)-entry is equal to ((di)p+(dj)p)1/pif vi～vj,and 0 otherwise,where di denotes the degree of vertex viin G.The matrix generalizes the famous Zagreb matrix(p=1),Sombor matrix (p=2) and inverse sum index matrix (p=-1).In this paper,we find a pair of p-Sombor noncospectral equienergetic graphs and determine some bounds for the p-Sombor(Laplacian) spectral radius.Then we describe the properties of connected graphs with k distinct p-Sombor Laplacian eigenvalues.At last,we determine the Sombor spectrum of some special graphs.As a by-product,we determine the spectral properties of Sombor matrix(p=2),Zagreb matrix(p=1) and inverse sum index matrix(p=-1).

关键词： p-Sombor matrix p-Sombor Laplacian matrix p-Sombor spectrum

Regular Graphs with a Complete Bipartite Graph as a Star Complement

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Journal of Mathematical Research with Applications 2023年第5期43卷 505-521页

作者： Xiaona FANG lihua you Rangwei WU Yufei HUANG School of Mathematical Sciences South China Normal University Department of Mathematics Teaching Guangzhou Civil Aviation College

Let G be a graph of order n and μ be an adjacency eigenvalue of G with multiplicity k ≥ 1. A star complement H for μ in G is an induced subgraph of G with n-k vertices and no eigenvalue μ, and the vertex subset X = V(G-H) is called a star set for μ in G. The star complement technique provides a spectral tool for reconstructing a certain part of a graph from the remaining part. In this paper, we study the regular graphs with Kt,s(s ≥ t ≥ 2) as a star complement for an eigenvalue μ, especially, characterize the case of t = 3 completely, obtain some properties when t = s, and propose some problems for further study.

关键词： adjacency eigenvalue star set star complement regular graph

Sharp bounds for spectral radius of nonnegative weakly irreducible tensors

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Frontiers of Mathematics in China 2019年第5期14卷 989-1015页

作者： lihua you Xiaohua HUANG Xiying YUAN School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China Department of Mathematics Shanghai UniversityShanghai 200444China

We obtain the sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor.By using the technique of the representation associate matrix of a tensor and the associate directed graph of the matrix,the equality cases of the bounds are completely characterized by graph theory methods.Applying these bounds to a nonnegative irreducible matrix or a connected graph(digraph),we can improve the results of L.H.you,Y.J.Shu,and P.Z.Yuan[Linear Multilinear Algebra,2017,65(1):113-128],and obtain some new or known results.Applying these bounds to a uniform hypergraph,we obtain some new results and improve some known results of X.Y.Yuan,M.Zhang,and M.Lu[Linear Algebra Appl.,2015,484:540-549].Finally,we give a characterization of a strongly connected/c-uniform directed hypergraph,and obtain some new results by applying these bounds to a uniform directed hypergraph.

关键词： Nonnegative weakly irreducible tensors uniform(directed)hypergraph spectral radius bound

The Smallest Hosoya Index of Bicyclic Graphs with Given Pendent Vertices

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Journal of Mathematical Research with Applications 2014年第1期34卷 12-32页

作者： lihua you Chaoxia WEI Zhifu you School of Mathematical Sciences South China Normal University School of Computer Science Guangdong Polytechnic Normal University

Let G be a graph.The Hosoya index Z(G)of a graph G is defined to be the total number of its matchings.In this paper,we characterize the graph with the smallest Hosoya index of bicyclic graphs with given pendent vertic... 详细信息

关键词： Hosoya index bicyclic graph pendent vertex matching.

The Maximum Balaban Index (Sum-Balaban Index) of Unicyclic Graphs

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Journal of Mathematical Research with Applications 2014年第4期34卷 392-402页

作者： lihua you Xin DONG School of Mathematical Sciences South China Normal UniversityGuangdong 510631P. R. China

The Balaban index of a connected graph G is defined as J(G) =|E(G)|μ + 1∑e=uv∈E(G)1√DG(u)DG(v),and the Sum-Balaban index is defined as SJ(G) =|E(G)|μ + 1∑e=uv∈E(G)1√DG(u)+DG(v),where DG(u) =∑w∈V(G)dG(u, w), and μ is the cyclomatic number of G. In this paper, the unicyclic graphs with the maximum Balaban index and the maximum Sum-Balaban index among all unicyclic graphs on n vertices are characterized, respectively.

关键词： Balaban index Sum-Balaban index unicyclic maximum.

The Characterization of Primitive Symmetric Signed Digraphs with the Second Maximum Base

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Journal of Mathematical Research with Applications 2013年第4期33卷 379-391页

作者： lihua you Shuyong YI School of Mathematical Sciences South China Normal University

Recently, the primitive symmetric signed digraphs on n vertices with the maximum base 2n and the primitive symmetric loop-free signed digraphs on n vertices with the maximum base 2n-1 are characterized, respectively. In this paper, the primitive symmetric signed digraphs with loops on n vertices with the base 2n-1 are characterized, and then the primitive symmetric signed digraphs on n vertices with the second maximum base 2n-1 are characterized.

关键词： matrix symmetric primitive non-powerful base signed digraph.

Primitive Non-Powerful Symmetric Loop-Free Signed Digraphs with Base 3 and Minimum Number of Arcs

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Journal of Mathematical Research with Applications 2013年第3期33卷 273-287页

作者： lihua you Yuhan WU School of Mathematical Sciences South China Normal University

Let S be a primitive non-powerful symmetric loop-free signed digraph on even n vertices with base 3 and minimum number of arcs. In [lihua you, Yuhan WU. Primitive non-powerful symmetric loop-free signed digraphs with given base and minimum number of arcs. Linear Algebra Appl., 2011, 434(5), 1215-1227], authors conjectured that D is the underlying digraph of S with exp(D) = 3 if and only if D is isomorphic to ED n,3,3 , where ED n,3,3 = (V, A) is a digraph with V = {1, 2, . . . , n}, A = {(1, i), (i, 1) | 3≤i≤n} ∪ {(2i-1, 2i), (2i, 2i-1) | 2≤i≤ n/2 } ∪ {(2, 3), (3, 2), (2, 4), (4, 2)}). In this paper, we show the conjecture is true and completely characterize the underlying digraphs which have base 3 and the minimum number of arcs.

关键词： primitive symmetric non-powerful base signed digraph.

广义Erdös-Straus猜想的互异正整数解的存在性

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数学理论与应用 2024年第2期44卷 65-79页

作者：尤利华李佳姻袁平之华南师范大学数学科学学院广州510631

本文研究当n>k≥2且t≥2时方程k/n=1/x_(1)+1/x_(2)+…+1/x_(t)的互异正整数解,证明若方程有正整数解,则至少有一互异正整数解;当k=5,t=3时,除了n≡1,5041,6301,8821,13861,15121(mod 16380)外方程有一互异正整数解;当n≥3,t=4时,除了n≡1,81901(mod 163800)外方程有一互异正整数解;并进一步指出对于任意的n(>k),当t≥k≥2时,方程至少有一互异正整数解.

关键词：不定方程正整数解互异 Erd?s-Straus 猜想

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基于高斯混合分布及EM算法的抗干扰定位方法

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航天电子对抗 2024年第1期40卷 18-26页

作者：初飞陈洪转由立华杨立南京航空航天大学经济与管理学院江苏南京210016 北京微电子技术研究所北京100076

针对当前导航接收机自主完好性监测算法(RAIM)在欺骗式干扰环境下,存在多故障识别能力弱、计算复杂度高等问题,提出一种基于高斯混合分布及EM算法的抗干扰定位方法,用于存在生成式、转发式欺骗干扰的复杂电子对抗环境。该方法提出一种... 详细信息

针对当前导航接收机自主完好性监测算法(RAIM)在欺骗式干扰环境下,存在多故障识别能力弱、计算复杂度高等问题,提出一种基于高斯混合分布及EM算法的抗干扰定位方法,用于存在生成式、转发式欺骗干扰的复杂电子对抗环境。该方法提出一种最小截尾平方和(LTS)估计的快速算法,从而得到高可靠的迭代初值,首次采用高斯混合分布建立极大似然估计模型,并使用EM算法对其进行求解得到可靠的定位结果,最终计算实时定位误差并实现多个干扰的识别。仿真结果表明,所提方法在干扰数量为10时,与MM估计方法相比定位精度提高53%,计算时间缩短到原先的1/5000,具有更高的定位精度以及更短的计算时间,可为电子对抗环境下的高可靠卫星应用提供支撑。

关键词：接收机自主完好性监测算法抗干扰非高斯稳健定位

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