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A line graph has an articulation point if and only if the underlying graph has a bridge for which neither endpoint has degree one. [2] For a graph G with n vertices and m edges, the number of vertices of the line graph L(G) is m, and the number of edges of L(G) is half the sum of the squares of the degrees of the vertices in G, minus m. [6]
where the zero and one entries of are treated as numerical, rather than logical as for simple graphs, values, explaining the difference in the results - for simple graphs, the symmetrized graph still needs to be simple with its symmetrized adjacency matrix having only logical, not numerical values, e.g., the logical sum is 1 v 1 = 1, while the ...
A number line is usually represented as being horizontal, but in a Cartesian coordinate plane the vertical axis (y-axis) is also a number line. [5] According to one convention, positive numbers always lie on the right side of zero, negative numbers always lie on the left side of zero, and arrowheads on both ends of the line are meant to suggest ...
A graph with six vertices and seven edges. In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points) and each of the related pairs of vertices ...
In the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences of mathematical logic. There are several variations in the types of logical operation that can be used in these sentences. The first-order logic of graphs concerns sentences in which the ...
A line chart or line graph, also known as curve chart, [1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [2] It is a basic type of chart common in many fields. It is similar to a scatter plot except that the measurement points are ordered (typically by their x-axis ...
If b = 0, the line is a vertical line (that is a line parallel to the y-axis) of equation =, which is not the graph of a function of x. Similarly, if a ≠ 0, the line is the graph of a function of y, and, if a = 0, one has a horizontal line of equation =.
Function. In mathematics, the graph of a function is the set of ordered pairs , where In the common case where and are real numbers, these pairs are Cartesian coordinates of points in a plane and often form a curve. The graphical representation of the graph of a function is also known as a plot. In the case of functions of two variables ...