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The star graphs K 1,3, K 1,4, K 1,5, and K 1,6. A complete bipartite graph of K 4,7 showing that Turán's brick factory problem with 4 storage sites (yellow spots) and 7 kilns (blue spots) requires 18 crossings (red dots) For any k, K 1,k is called a star. [2] All complete bipartite graphs which are trees are stars. The graph K 1,3 is called a ...
K n can be decomposed into n trees T i such that T i has i vertices. [6] Ringel's conjecture asks if the complete graph K 2n+1 can be decomposed into copies of any tree with n edges. [7] This is known to be true for sufficiently large n. [8] [9] The number of all distinct paths between a specific pair of vertices in K n+2 is given [10] by
Parts I and V of the book contain descriptions of clock designs. The rest of the book is made of three, highly abstract, mathematical and mechanical parts dealing with pendular motion and a theory of curves. [1] Except for Part IV, written in 1664, the entirety of the book was composed in a three-month period starting in October 1659. [4] [5]
dc is the oldest surviving Unix language program. When its home Bell Labs received a PDP-11, dc—written in B—was the first language to run on the new computer, even before an assembler. [2]
NuCalc 1.0 is for 680x0 Macintosh. In 2005, This American Life featured Avitzur's story in episode 284, Should I Stay or Should I go?. [2] At one time, it was a free download for Mac OS 9, Mac OS X 10.3, and Mac OS X 10.4. However, these may lack some features of 1.0 and may include promotion for the more advanced, commercial version of the ...
D 1 is isomorphic to Z 2, the cyclic group of order 2. D 2 is isomorphic to K 4, the Klein four-group. D 1 and D 2 are exceptional in that: D 1 and D 2 are the only abelian dihedral groups. Otherwise, D n is non-abelian. D n is a subgroup of the symmetric group S n for n ≥ 3. Since 2n > n! for n = 1 or n = 2, for these values, D n is too ...
Particular examples of k-periodic number theoretic functions are the Dirichlet characters = modulo k and the greatest common divisor function () = (,). It is known that every k-periodic arithmetic function has a representation as a finite discrete Fourier series of the form
The Johnson graph J(n, k) is the graph whose vertices are the k-element subsets of an n-element set, two vertices being adjacent when they meet in a (k − 1)-element set. The Johnson graph J(n, 2) is the complement of the Kneser graph K(n, 2). Johnson graphs are closely related to the Johnson scheme, both of which are named after Selmer M. Johnson