Search results
Results from the WOW.Com Content Network
The California Job Case was a compartmentalized box for printing in the 19th century, sizes corresponding to the commonality of letters. The frequency of letters in text has been studied for use in cryptanalysis, and frequency analysis in particular, dating back to the Arab mathematician al-Kindi (c. AD 801–873 ), who formally developed the method (the ciphers breakable by this technique go ...
While each non-complete word-representable graph G is 2(n − κ(G))-representable, where κ(G) is the size of a maximal clique in G, [7] the highest known representation number is floor(n/2) given by crown graphs with an all-adjacent vertex. [7] Interestingly, such graphs are not the only graphs that require long representations. [15]
A word equation is a formal equality:= = between a pair of words and , each over an alphabet comprising both constants (c.f. ) and unknowns (c.f. ). [1] An assignment h {\displaystyle h} of constant words to the unknowns of E {\displaystyle E} is said to solve E {\displaystyle E} if it maps both sides of E {\displaystyle E} to identical words.
Some sources claim that the letter K in this notation stands for the German word komplett, [4] but the German name for a complete graph, vollständiger Graph, does not contain the letter K, and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory. [5] K n has n(n – 1)/2 edges (a triangular ...
For example, if x, y and z are elements of a group G, then xy, z −1 xzz and y −1 zxx −1 yz −1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, [1] or even in every group. [2] Words play an important role in the theory of free groups and presentations, and are central objects of study in ...
A trivial graph is a graph with 0 or 1 vertices. [16] A graph with 0 vertices is also called null graph. Turán 1. Pál Turán 2. A Turán graph is a balanced complete multipartite graph. 3. Turán's theorem states that Turán graphs have the maximum number of edges among all clique-free graphs of a given order. 4.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
A graph is planar if it contains as a subdivision neither the complete bipartite graph K 3,3 nor the complete graph K 5. Another problem in subdivision containment is the Kelmans–Seymour conjecture: Every 5-vertex-connected graph that is not planar contains a subdivision of the 5-vertex complete graph K 5.