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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 complete graph K 4 has ten matchings, corresponding to the value T(4) = 10 of the fourth telephone number. In mathematics, the telephone numbers or the involution numbers form a sequence of integers that count the ways n people can be connected by person-to-person telephone calls.
Note that property (1) implies that the zig-zag product of two expander graphs is also an expander graph, thus zig-zag products can be used inductively to create a family of expander graphs. Intuitively, the construction of the zig-zag product can be thought of in the following way.
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). Cubic graphs have slope number at most four, but graphs of degree five may have unbounded slope number; it remains open whether the slope number of degree-4 graphs is bounded. [12]
As cold weather persists in Northeast Ohio, the Akron Home and Garden Show at the Knight Center will have you looking forward to spring.
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:
According to Freddie Mac's latest forecast, home prices will rise 2.1% in 2024 and 0.6% in 2025.
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. [1]