A5042907172- Limits and Structures in Graph Theory
- Advanced Graph Theory Research
- Graph theory and applications
- Graph Labeling and Dimension Problems
- graph theory and CDMA systems
- Finite Group Theory Research
- Interconnection Networks and Systems
- Matrix Theory and Algorithms
- Analytic Number Theory Research
- Advanced Topology and Set Theory
- Graph Theory and Algorithms
- Advanced Combinatorial Mathematics
- Advanced Mathematical Identities
- Advanced Computational Techniques and Applications
- Synthesis and Properties of Aromatic Compounds
- Complex Network Analysis Techniques
- Free Radicals and Antioxidants
- Spectral Theory in Mathematical Physics
- Network Security and Intrusion Detection
- Complexity and Algorithms in Graphs
- Mathematical Dynamics and Fractals
- Handwritten Text Recognition Techniques
- Fusion and Plasma Physics Studies
- Consumer Packaging Perceptions and Trends
- Organometallic Complex Synthesis and Catalysis
Nankai University
2019-2025
Northwestern Polytechnical University
2013-2023
Shenyang Sport University
2023
Dalian Maritime University
2017-2023
Hudson Institute
2020-2023
Beibu Gulf University
2023
Commercial Aircraft Corporation of China (China)
2022
Tianjin University
2013-2020
Hebei University of Technology
2013
Jilin Normal University
2011
Bollob\'as and Nikiforov [J. Combin. Theory, Ser. B. 97 (2007) 859--865] conjectured the following. If $G$ is a $K_{r+1}$-free graph on at least $r+1$ vertices $m$ edges, then $\lambda^2_1(G)+\lambda^2_2(G)\leq \frac{r-1}{r}\cdot2m$, where $\lambda_1(G)$ $\lambda_2(G)$ are largest second eigenvalues of adjacency matrix $A(G)$, respectively. In this paper, we confirm conjecture in case $r=2$, by using tools from doubly stochastic theory, also characterize all families extremal graphs....
In 1962, Erdős gave a sufficient condition for Hamilton cycles in terms of the vertex number, edge number and minimum degree graphs which generalized Ore's theorem. One year later, Moon Moser an analogous result balanced bipartite graphs. this paper, we present spectral analogues Erdős' theorem Moon–Moser's theorem, respectively. Let be class non-Hamiltonian order n at least k. We determine maximum (signless Laplacian) radius (for large enough n), complements . All extremal with are...
Let be a graph with minimum degree . The spectral radius of , denoted by is the largest eigenvalue adjacency matrix In this note, we mainly prove following two results.(1) on vertices If then contains Hamilton path unless .(2) cycle As corollaries our first result, previous theorems due to Fiedler and Nikiforov Lu et al. are obtained, respectively. Our second result refines another theorem Nikiforov.
The famous Erd\H{o}s-Gallai Theorem on the Tur\'an number of paths states that every graph with $n$ vertices and $m$ edges contains a path at least $\frac{2m}{n}$ edges. In this note, we first establish simple but novel extension by proving $G$ $\frac{(s+1)N_{s+1}(G)}{N_{s}(G)}+s-1$ edges, where $N_j(G)$ denotes $j$-cliques in for $1\leq j\leq\omega(G)$. We also construct family graphs which shows our improves estimate given Theorem. Among applications, show, example, main results...
In 1990, Cvetkovi\'{c} and Rowlinson [The largest eigenvalue of a graph: survey, Linear Multilinear Algebra 28(1-2) (1990), 3--33] conjectured that among all outerplanar graphs on $n$ vertices, $K_1\vee P_{n-1}$ attains the maximum spectral radius. 2017, Tait Tobin [Three conjectures in extremal graph theory, J. Combin. Theory, Ser. B 126 (2017) 137-161] confirmed conjecture for sufficiently large values $n$. this article, we show is true $n\geq2$ except $n=6$.
Abstract As the counterpart of classical theorems on cycles consecutive lengths due to Bondy and Bollobás in spectral graph theory, Nikiforov proposed following open problem 2008: What is maximum such that for all positive sufficiently large , every order with radius contains a cycle length each integer . We prove improving existing bounds. Besides several novel ideas, our proof technique partly inspired by recent research Ramsey numbers star versus even Allen, Łuczak, Polcyn, Zhang, aid...
Spectral graph theory is a captivating area of that employs the eigenvalues and eigenvectors matrices associated with graphs to study them. In this paper, we present collection $20$ topics in spectral theory, covering range open problems conjectures. Our focus primarily on adjacency matrix graphs, for each topic, provide brief historical overview.
In this paper, we prove tight sufficient conditions for traceability and Hamiltonicity of connected graphs with given minimum degree, in terms Wiener index Harary index. We also some result on balanced bipartite the similar fashion. two recent papers \cite{LDJ2016,LDJ2017}, Liu et al. corrected previous work index, respectively, such as \cite{HW2013,Y2013}. generalize these results give short unified proofs. All paper are best possible.
Let $G$ be a connected claw-free graph on $n$ vertices and $\overline{G}$ its complement graph. $μ(G)$ the spectral radius of $G$. Denote by $N_{n-3,3}$ consisting $K_{n-3}$ three disjoint pendent edges. In this note we prove that: (1) If $μ(G)\geq n-4$, then is traceable unless $G=N_{n-3,3}$. (2) $μ(\overline{G})\leq μ(\overline{N_{n-3,3}})$ $n\geq 24$, Our works are counterparts graphs previous theorems due to Lu et al., Fiedler Nikiforov, respectively.
In this paper, we first present spectral conditions for the existence of $C_{n-1}$ in graphs (2-connected graphs) order $n$, which are motivated by a conjecture Erd\H{o}s. Then prove Hamilton cycles balanced bipartite graphs. This result presents analog Moon-Moser's theorem on graphs, and extends previous due to Li second author $n$ sufficiently large. We conclude paper with two problems tight long given lengths.
Let $\cal H$ be a family of graphs. The Tur\'an number ${\rm ex}(n,{\cal H})$ is the maximum possible edges in an $n$-vertex graph which does not contain any member as subgraph. As common generalization Tur\'an's theorem and Erd\H{o}s-Gallai on matchings, Alon Frankl determined for ${\cal H}=\{K_r,M_k\}$, where $M_k$ matching size $k$. Replacing by $P_k$, Katona Xiao obtained H}=\{K_r,P_k\}$ $r \leq \lfloor k/2 \rfloor$ sufficiently large $n$. In addition, they proposed conjecture case \geq...