Vertex degree

The main contents of "Lecture Design and Analysis of Algorithms: Lecture 27" include all of the following: Fractional knapsack problem, introduction to graphs, graphs and digraphs, incident edge, degree of a vertex, adjacent vertices, fractional knapsack problem.

31p youzhangjing_1909 28-04-2022 10 2   Download

The main contents of "Lecture Design and Analysis of Algorithms: Lecture 28" include all of the following: Degree of a vertex, observations about graphs, paths and cycles, graph representations, shortest path.

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The betweenness centrality (BWC) of a vertex is a measure of the fraction of shortest paths between any two vertices going through the vertex and is one of the widely used shortest path-based centrality metrics for the complex network analysis.

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In the paper, we first point out that Theorems 1, 2, and 4 are incorrect and in this short note we present the correct inequalities for Randic and GA indices. In the same paper, we provide the equality cases for Theorems 3, 5, and 6.

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In this paper, we obtain, analyze, and compare various lower bounds for the forgotten topological index involving the number of vertices, edges, and maximum and minimum vertex degree. Then we give Nordhaus–Gaddumtype inequalities for the forgotten topological index and coindex. Finally, we correct the number of extremal chemical trees on 15 vertices.

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This is an electronic version of the second (2000) edition of the above Springer book, from their series Graduate Texts in Mathematics, vol. 173. The cross-references in the text and in the margins are active links: click on them to be taken to the appropriate page. The printed edition of this book can be ordered from your bookseller, or electronically from Springer through the Web sites referred to below.

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Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Bootstrap Percolation and Diffusion in Random Graphs with Given Vertex Degrees...

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We propose two alternative measures of the local irregularity of a graph in terms of its vertex degrees and relate these measures to the order and the global irregularity of the graph measured by the difference of its maximum and minimum vertex degree.All graphs will be simple and finite. Let G = (V,E) be a graph of order n = |V |. The degree and the neighbourhood of a vertex u 2 V will be denoted by d(u) and N(u). The maximum and minimum degree of G will be denoted by
(G) and (G).

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Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees...

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Đồ thị vô hướng (undirected graph) Đỉnh (vertex) Cạnh (edge) {1,4} Số đỉnh n = 4. Số cạnh m = 5. “Đỉnh 2 và đỉnh 3 kề nhau (adjacent)” (adjacent)” Đa đồ thị, Đồ thị đơn (simple graph) Khuyên (loop) Đồ thị G(V, E) Tập đỉnh V = {1, 2, 3, 4} Tập cạnh: E = {12, 13, 14, 23, 34} ‘Đơn’ = Không có cạnh song song và không có khuyên Hai cạnh song song (parallel) Đồ thị có hướng (directed graph) Khuyên (loop) Cung (arc) [1,2] Đỉnh đầu (initial) Đỉnh cuối (terminal) Bậc của đỉnh trong đồ thị vô hướng Định nghĩa: Bậc (degree) của một đỉnh x là số...

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Classification of Mechanisms Using graph representation, mechanism structures can be conveniently represented by graphs. The classification problem can be transformed into an enumeration of nonisomorphic graphs for a prescribed number of degrees of freedom, number of loops, number of vertices, and number of edges. The degrees of freedom of a mechanism are governed by Equation (4.3). The number of loops, number of links, and number of joints in a mechanism are related by Euler’s equation, Equation (4.5). The loop mobility criterion is given by Equation (4.7).

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This appendix provides an atlas of epicyclic gear trains classified according to the number of degrees of freedom, the number of independent loops, and the vertex degree listings. Both labeled graphs and typical functional schematic diagrams are sketched.

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This appendix provides an atlas of planar linkages classified according to the number of degrees of freedom, the number of independent loops, the vertex degree listings, and the corresponding contract graphs.

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