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学者姓名：刘剑萍
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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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对实数α∈[0,1],图G的Aα-矩阵定义为Aα(G)=αD(G)+(1-α)A(G),其中D(G)和A(G)分别是G的度矩阵和邻接矩阵.如果与G是Aα-同谱的图都与G同构,则称G是Aα-谱确定的.将星图的中心与圈图的一个顶点粘合所得到的图称为章鱼图,由s个三角形共同粘结在路上的一个端点所得到的图称为风轮图.该文证明了对任意α ∈(2/3,1),章鱼图和风轮图都是A.-谱确定的.
Keyword ：
Aα-谱 Aα-谱 同谱图 同谱图 章鱼图 章鱼图 谱确定 谱确定 风轮图 风轮图
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| GB/T 7714 | 刘剑萍 , 陈鸿麒 . 章鱼图和风轮图的Aα-谱确定问题 [J]. | 南宁师范大学学报（自然科学版） , 2024 , 41 (1) : 1-6 . |
| MLA | 刘剑萍 et al. "章鱼图和风轮图的Aα-谱确定问题" . | 南宁师范大学学报（自然科学版） 41 . 1 (2024) : 1-6 . |
| APA | 刘剑萍 , 陈鸿麒 . 章鱼图和风轮图的Aα-谱确定问题 . | 南宁师范大学学报（自然科学版） , 2024 , 41 (1) , 1-6 . |
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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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对实数α∈[0,1],图G的A
Keyword ：
A A
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| GB/T 7714 | 刘剑萍 , 陈鸿麒 . 章鱼图和风轮图的A [J]. | 南宁师范大学学报(自然科学版) , 2024 , 41 (01) : 1-6 . |
| MLA | 刘剑萍 et al. "章鱼图和风轮图的A" . | 南宁师范大学学报(自然科学版) 41 . 01 (2024) : 1-6 . |
| APA | 刘剑萍 , 陈鸿麒 . 章鱼图和风轮图的A . | 南宁师范大学学报(自然科学版) , 2024 , 41 (01) , 1-6 . |
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A k-cone c-cyclic graph is the join of the complete graph K-k and a c-cyclic graph (if k = 0, we get the usual connected graph). A k-apex tree (resp., k-apex unicyclic graph) is defined as a connected graph G with a k-subset V-k subset of V(G) such that G - V-k is a tree (resp., unicylic graph), but G - X is not a tree (resp., unicylic graph) for any X subset of V(G) with vertical bar X vertical bar < k. In this paper, we extend those extremal results and majorization theorems concerning connected graphs of Liu et al. (2019) to k-cone c-cyclic graphs. We also use a unified method to characterize the extremal maximum and minimum results of many topological indices in the class of k-apex trees and k-apex unicyclic graphs, respectively. The later results extend the main results of Javaid et al. (2019); Liu et al. (2020) and partially answer the open problem of Javaid et al. (2019). Except for the new majorization theorem, some new techniques are also established to deal with the minimum extremal results of this paper. (C) 2020 Elsevier B.V. All rights reserved.
Keyword ：
BFS-graph BFS-graph Degree sequence Degree sequence k-apex tree k-apex tree k-apex unicyclic graph k-apex unicyclic graph k-cone c-cyclic graph k-cone c-cyclic graph Majorization Majorization
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| GB/T 7714 | Liu, Muhuo , Tomescu, Ioan , Liu, Jianping . Unified extremal results for k-apex unicyclic graphs (trees) [J]. | DISCRETE APPLIED MATHEMATICS , 2021 , 288 : 35-49 . |
| MLA | Liu, Muhuo et al. "Unified extremal results for k-apex unicyclic graphs (trees)" . | DISCRETE APPLIED MATHEMATICS 288 (2021) : 35-49 . |
| APA | Liu, Muhuo , Tomescu, Ioan , Liu, Jianping . Unified extremal results for k-apex unicyclic graphs (trees) . | DISCRETE APPLIED MATHEMATICS , 2021 , 288 , 35-49 . |
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As a generalization of the famous atom-bond connectivity index ABC(G), the general atom-bound connectivity index of a graph G, ABC(alpha)(G), is denoted by ABC(alpha)(G) = Sigma(uv is an element of E(G)) (d(G)(u) + d(G)(v) -2/d(G)(u)d(G)(v))(alpha) for any alpha is an element of R \ {0}. The (general) atom-bound connectivity index has been shown to be a useful topological index and has received more and more attention recently. In this paper, we show that ABC(alpha)(G + uv) > ABC(alpha)(G) holds for any two non-adjacent vertices u and v of a graph G with d(G)(u) + d(G)(v) >= 1 for 0 < alpha <= 1/2. Moreover, by applying this new property, we determine the maximum value of ABC(alpha) together with the corresponding extremal graphs in the class of graphs with n vertices and maximum degree Delta for 0 < alpha <= 1/2.
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| GB/T 7714 | Tan, Xuegong , Liu, Muhuo , Liu, Jianping . On the Maximal General ABC Index of Graphs with Fixed Maximum Degree [J]. | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY , 2021 , 85 (1) : 121-130 . |
| MLA | Tan, Xuegong et al. "On the Maximal General ABC Index of Graphs with Fixed Maximum Degree" . | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY 85 . 1 (2021) : 121-130 . |
| APA | Tan, Xuegong , Liu, Muhuo , Liu, Jianping . On the Maximal General ABC Index of Graphs with Fixed Maximum Degree . | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY , 2021 , 85 (1) , 121-130 . |
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给定2个图G1和G2,设G1的边集E(G1)={e1,e2,…,emi},则图G1⊙G2可由一个G1,m1个G2通过在G1对应的每条边外加一个孤立点,新增加的点记为U={u1,u2,…,um1},将ui分别与第i个G2的所有点以及G1中的边ei的端点相连得到,其中i=1,2,…,m1.得到:(i)当G1是正则图,G2是正则图或完全二部图时,确定了G1⊙G2的邻接谱(A-谱).(ii)当G1是正则图,G2是任意图时,给出了G1⊙G2的拉普拉斯谱(L-谱).(iii)当G1和G2都是正则图时,给出了G1⊙G2的无符号拉普拉斯谱(Q-谱).作为以上结论的应用,构建了无限多对A-同谱图、L-同谱图和Q-同谱图;同时当G1是正则图时,确定了G1⊙G2支撑树的数量和Kirchhoff指数.
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 (2) : 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 . 2 (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 (2) , 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 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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