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学者姓名：陈锦松
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Let G(alpha) be the graph obtained from a simple graph G of order n by adding sigma self-loops, one self-loop at each vertex in S subset of V (G). Let lambda(1)(G(sigma)), lambda(2)(G(sigma)),...,lambda(n)(G(sigma)) be the eigenvalues of G(sigma). The energy of G(sigma), denoted by E (G(sigma)), is defined as E (G(sigma)) = (i=1)Sigma(n) vertical bar lambda(i)(G(sigma)) -sigma/n vertical bar. In this paper, using various analytic inequalities and previously established results, we derive several new lower and upper bounds on E(G(sigma)).
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| GB/T 7714 | Liu, Jianping , Chen, Yingni , Dimitrov, Darko et al. New Bounds on the Energy of Graphs with Self-Loops [J]. | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY , 2024 , 91 (3) : 779-796 . |
| MLA | Liu, Jianping et al. "New Bounds on the Energy of Graphs with Self-Loops" . | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY 91 . 3 (2024) : 779-796 . |
| APA | Liu, Jianping , Chen, Yingni , Dimitrov, Darko , Chen, Jinsong . New Bounds on the Energy of Graphs with Self-Loops . | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY , 2024 , 91 (3) , 779-796 . |
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图G的能量E(G)定义为G的邻接矩阵的所有特征值的绝对值之和.一个n阶图如果它的能量等于n,则称为阶能量图.结合图与矩阵的运算,特别是矩阵的Kronecker积,给出图的一个新的运算.进一步确定相应新图的谱;并应用该运算由给定的某些非阶能量图,构造出一系列新的阶能量图族;还由任意阶能量图,构造出 3 类新的阶能量图族.
Keyword ：
Kronecker积 Kronecker积 图的运算 图的运算 能量 能量 阶能量图 阶能量图
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| GB/T 7714 | 陈锦松 , 杨书若月 , 刘剑萍 . 图的一个运算及其在阶能量图上的应用 [J]. | 福州大学学报（自然科学版） , 2024 , 52 (6) : 635-638 . |
| MLA | 陈锦松 et al. "图的一个运算及其在阶能量图上的应用" . | 福州大学学报（自然科学版） 52 . 6 (2024) : 635-638 . |
| APA | 陈锦松 , 杨书若月 , 刘剑萍 . 图的一个运算及其在阶能量图上的应用 . | 福州大学学报（自然科学版） , 2024 , 52 (6) , 635-638 . |
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A natural extension of the well-known Albertson irregularity of graphs is the so-called sigma-irregularity. For a simple graph G, it is defined as sigma(G) = Sigma(uv is an element of E(G))(d(G)(u) - d(G)(v))(2), where d(G)(v) denotes the degree of a vertex v of G. In this study, we characterize trees with minimal and maximal sigma-irregularity among trees with a given degree sequence. Specifically, we show that greedy trees minimize sigma-irregularity, while adopting trees maximize it among trees with a prescribed degree sequence.
Keyword ：
extremal trees extremal trees irregularity measures irregularity measures irregularity (of graph) irregularity (of graph) sigma-irregularity sigma-irregularity
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| GB/T 7714 | Dimitrov, Darko , Gao, Wei , Lin, Wenshui et al. Extremal trees with fixed degree sequence for σ-irregularity [J]. | DISCRETE MATHEMATICS LETTERS , 2023 , 12 : 166-172 . |
| MLA | Dimitrov, Darko et al. "Extremal trees with fixed degree sequence for σ-irregularity" . | DISCRETE MATHEMATICS LETTERS 12 (2023) : 166-172 . |
| APA | Dimitrov, Darko , Gao, Wei , Lin, Wenshui , Chen, Jinsong . Extremal trees with fixed degree sequence for σ-irregularity . | DISCRETE MATHEMATICS LETTERS , 2023 , 12 , 166-172 . |
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给定2个图G_1和G_2,设G_1的边集E (G_1)={e_1,e_2,?,em_1},则图G_1⊙G_2可由一个G_1,m_1个G_2通过在G_1对应的每条边外加一个孤立点,新增加的点记为U={u_1,u_2,?,um_1},将u_i分别与第i个G_2的所有点以及G_1中的边ei的端点相连得到,其中i=1,2,?,m_1。得到:(i)当G_1是正则图,G_2是正则图或完全二部图时,确定了G_1⊙G_2的邻接谱(A-谱)。(ii)当G_1是正则图,G_2是任意图时,给出了G_1⊙G_2的拉普拉斯谱(L-谱)。(iii)当G_1和G_2都是正则图时,给出了G_1⊙G_2的无符号拉普拉斯谱(Q-...
Keyword ：
同谱图 同谱图 基尔霍夫(Kirchhoff)指数 基尔霍夫(Kirchhoff)指数 支撑树 支撑树 谱 谱
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| GB/T 7714 | 刘剑萍 , 吴先章 , 陈锦松 . 关于两个图的一类新连接图的谱 [J]. | 浙江大学学报(理学版) , 2021 , 48 (02) : 180-188,195 . |
| MLA | 刘剑萍 et al. "关于两个图的一类新连接图的谱" . | 浙江大学学报(理学版) 48 . 02 (2021) : 180-188,195 . |
| APA | 刘剑萍 , 吴先章 , 陈锦松 . 关于两个图的一类新连接图的谱 . | 浙江大学学报(理学版) , 2021 , 48 (02) , 180-188,195 . |
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The general atom-bond connectivity index (ABCα) of a graph G = (V, E) is defined as ABCα(G) = 'Equation Presented', where uν is an edge of G, duis the degree of the vertex u, α is an arbitrary nonzero real number, and G has no isolated K2if a < 0. In this paper, we will determine the upper bound (resp. the lower bound) of ABCαindex for α ∈ (0, 1] (resp. for α ∈ (-∞, 0)) among all connected graphs with fixed maximum degree, and characterize the corresponding extremal graphs. © 2020 University of Kragujevac, Faculty of Science. All rights reserved.
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| GB/T 7714 | Zheng, R. , Liu, J. , Chen, J. et al. Bounds on the general atom-bond connectivity indices [J]. | Match , 2020 , 83 (1) : 143-166 . |
| MLA | Zheng, R. et al. "Bounds on the general atom-bond connectivity indices" . | Match 83 . 1 (2020) : 143-166 . |
| APA | Zheng, R. , Liu, J. , Chen, J. , Liu, B. . Bounds on the general atom-bond connectivity indices . | Match , 2020 , 83 (1) , 143-166 . |
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The general atom-bond connectivity index (ABC(alpha)) of a graph G = (V, E) is defined as ABC(alpha)(G) = Sigma(uv is an element of E) (d(u) + d(v) - 2/d(u)d(v))(alpha), where uv is an edge of G, d(u) is the degree of the vertex u, alpha is an arbitrary nonzero real number, and G has no isolated K-2 if alpha < 0. In this paper, we will determine the upper bound (resp. the lower bound) of ABC(alpha) index for alpha is an element of (0, 1] (resp. for alpha is an element of (-infinity, 0)) among all connected graphs with fixed maximum degree, and characterize the corresponding extremal graphs.
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| GB/T 7714 | Zheng, Ruiling , Liu, Jianping , Chen, Jinsong et al. Bounds on the General Atom-Bond Connectivity Indices [J]. | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY , 2020 , 83 (1) : 143-166 . |
| MLA | Zheng, Ruiling et al. "Bounds on the General Atom-Bond Connectivity Indices" . | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY 83 . 1 (2020) : 143-166 . |
| APA | Zheng, Ruiling , Liu, Jianping , Chen, Jinsong , Liu, Bolian . Bounds on the General Atom-Bond Connectivity Indices . | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY , 2020 , 83 (1) , 143-166 . |
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The general atom bond connectivity index (ABC(alpha)) of a graph G = (V, E) is defined as ABC(alpha)(G) = Sigma(uv is an element of E(G)) (d(u) + d(v) - 2/d(u)d(v))(alpha), where uv is an edge of G, d(u) is the degree of the vertex u, alpha is an arbitrary nonzero real number, and G has no isolated K-2 if alpha < 0. In this paper, we determine the n-vertex (n >= 4) unicyclic graphs with maximal and second-maximal (resp. minimal and second-minimal) ABC(alpha) indices for alpha > 0 (resp. -3 <= alpha < 0). And the n-vertex (n >= 4) bicyclic graphs in which the ABC(alpha) index attains maximal (resp. minimal) value for alpha > 0 (resp. -1 <= alpha < 0) are also obtained.
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| GB/T 7714 | Liu, Jianping , Zheng, Ruiling , Chen, Jinsong et al. The Extremal General Atom-Bond Connectivity Indices of Unicyclic and Bicyclic Graphs [J]. | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY , 2019 , 81 (2) : 345-360 . |
| MLA | Liu, Jianping et al. "The Extremal General Atom-Bond Connectivity Indices of Unicyclic and Bicyclic Graphs" . | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY 81 . 2 (2019) : 345-360 . |
| APA | Liu, Jianping , Zheng, Ruiling , Chen, Jinsong , Liu, Bolian . The Extremal General Atom-Bond Connectivity Indices of Unicyclic and Bicyclic Graphs . | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY , 2019 , 81 (2) , 345-360 . |
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Let (D) be the A. spectral radius of digraph D, and let f be the set of digraphs with order n and dichromatic number r. In this paper, we characterize the digraph which has the maximal A. spectral radius in Moreover, we also determine the unique digraph which attains the maximum (resp. minimum) Ac, spectral radius among all strongly connected bicyclic digraphs. (C) 2018 Elsevier Inc. All rights reserved.
Keyword ：
A(alpha) spectral radius A(alpha) spectral radius Dichromatic number Dichromatic number infinity-digraph infinity-digraph theta-digraph theta-digraph
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| GB/T 7714 | Liu, Jianping , Wu, Xianzhang , Chen, Jinsong et al. The A, spectral radius characterization of some digraphs [J]. | LINEAR ALGEBRA AND ITS APPLICATIONS , 2019 , 563 : 63-74 . |
| MLA | Liu, Jianping et al. "The A, spectral radius characterization of some digraphs" . | LINEAR ALGEBRA AND ITS APPLICATIONS 563 (2019) : 63-74 . |
| APA | Liu, Jianping , Wu, Xianzhang , Chen, Jinsong , Liu, Bolian . The A, spectral radius characterization of some digraphs . | LINEAR ALGEBRA AND ITS APPLICATIONS , 2019 , 563 , 63-74 . |
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The general atom–bond connectivity index (ABC α ) of a graph G = (V, E) is defined as (formula pergented). where uv is an edge of G, d u is the degree of the vertex u, α is an arbitrary nonzero real number, and G has no isolated K 2 if α < 0. In this paper, we determine the n-vertex (n ≥ 4) unicyclic graphs with maximal and second-maximal (resp. minimal and second-minimal) ABC α indices for α > 0 (resp. −3 ≤ α < 0). And the n-vertex (n ≥ 4) bicyclic graphs in which the ABC α index attains maximal (resp. minimal) value for α > 0 (resp. −1 ≤ α < 0) are also obtained. © 2019 University of Kragujevac, Faculty of Science. All rights reserved.
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| GB/T 7714 | Liu, J. , Zheng, R. , Chen, J. et al. The extremal general atom–bond connectivity indices of unicyclic and bicyclic graphs ∗ [J]. | Match , 2019 , 81 (2) : 345-360 . |
| MLA | Liu, J. et al. "The extremal general atom–bond connectivity indices of unicyclic and bicyclic graphs ∗" . | Match 81 . 2 (2019) : 345-360 . |
| APA | Liu, J. , Zheng, R. , Chen, J. , Liu, B. . The extremal general atom–bond connectivity indices of unicyclic and bicyclic graphs ∗ . | Match , 2019 , 81 (2) , 345-360 . |
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Let G = (V, E) be a connected graph and P be graph-theoretic property. A network is often modeled by a graph G = (V, E). One fundamental consideration in the design of networks is reliability. The connectivity is an important parameter to measure the fault tolerance and reliability of network. The conditional connectivity lambda(G, P) or kappa(G, P) is the minimum cardinality of a set of edges or vertices, if it exists, whose deletion disconnects G and each remaining component has property P. Let F be a vertex set or edge set of G and P be the property of with at least k components. Then we have the k-component connectivity c kappa (k)(G) and the k-component edge connectivity c lambda(k)(G). In this paper, we determine the k-component (edge) connectivity of locally twisted cubes LTQ(n) for small k, and we also prove other properties of LTQ(n). (C) 2018 Elsevier Inc. All rights reserved.
Keyword ：
Conditional connectivity Conditional connectivity Fault tolerance Fault tolerance Interconnection networks Interconnection networks k-component connectivity k-component connectivity
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| GB/T 7714 | Guo, Litao , Su, Guifu , Lin, Wenshui et al. Fault tolerance of locally twisted cubes [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2018 , 334 : 401-406 . |
| MLA | Guo, Litao et al. "Fault tolerance of locally twisted cubes" . | APPLIED MATHEMATICS AND COMPUTATION 334 (2018) : 401-406 . |
| APA | Guo, Litao , Su, Guifu , Lin, Wenshui , Chen, Jinsong . Fault tolerance of locally twisted cubes . | APPLIED MATHEMATICS AND COMPUTATION , 2018 , 334 , 401-406 . |
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