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The zigzag product was introduced by Reingold, Vadhan & Wigderson (2000). When the zig-zag product was first introduced, it was used for the explicit construction of constant degree expanders and extractors. Later on, the zig-zag product was used in computational complexity theory to prove that symmetric logspace and logspace are equal ...
The trace of a triangle wave or a sawtooth wave is a zigzag. Pinking shears are designed to cut cloth or paper with a zigzag edge, to lessen fraying. [2] In sewing, a zigzag stitch is a machine stitch in a zigzag pattern. [3] The zigzag arch is an architectural embellishment used in Islamic, Byzantine, Norman and Romanesque architecture. [4] [5]
Line chart showing the population of the town of Pushkin, Saint Petersburg from 1800 to 2010, measured at various intervals. 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]
In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. [3] A contour map is a map illustrated with contour lines, for example a topographic map , which thus shows valleys and hills, and the steepness or gentleness of slopes. [ 4 ]
If a graph has vertices with high degree then it necessarily will have small angular resolution, but the angular resolution can be bounded below by a function of the degree. [12] The slope number of a graph is the minimum number of distinct edge slopes needed in a drawing with straight line segment edges (allowing crossings).
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G).
The incidence posets of path graphs form examples of fences. A linear extension of a fence is called an alternating permutation; André's problem of counting the number of different linear extensions has been studied since the 19th century. [1] The solutions to this counting problem, the so-called Euler zigzag numbers or up/down numbers, are:
This line has been called the amphoteric line, [2] the metal-nonmetal line, [3] the metalloid line, [4] [5] the semimetal line, [6] or the staircase. [2] [n 1] While it has also been called the Zintl border [8] or the Zintl line [9] [10] these terms instead refer to a vertical line sometimes drawn between groups 13 and 14.