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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]
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 ...
The open neighborhood of v in G may be denoted N G (v) or N(v), and the closed neighborhood may be denoted N G [v] or N[v]. When the openness or closedness of a neighborhood is not specified, it is assumed to be open. network A graph in which attributes (e.g. names) are associated with the nodes and/or edges. node A synonym for vertex. non-edge
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).
pseudo-blend = an abbreviation whose extra or omitted letters mean that it cannot stand as a true acronym, initialism, or portmanteau (a word formed by combining two or more words). (a) = acronym, e.g.: SARS – (a) severe acute respiratory syndrome (i) = initialism, e.g.: CD – (i) compact disc
If np < 1, then a graph in G(n, p) will almost surely have no connected components of size larger than O(log(n)). If np = 1, then a graph in G(n, p) will almost surely have a largest component whose size is of order n 2/3. If np → c > 1, where c is a constant, then a graph in G(n, p) will almost surely have a unique giant component containing ...
In the mathematical field of algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the degree of each vertex—that is, the number of edges attached to each vertex. [1]
His father was Everitt George Dunne Murray [3] (1890–1964), [4] who was a professor of bacteriology at Montreal's McGill University [5] from 1930 to 1955. After his childhood years in England and attending boarding school at Summer Fields in Oxford, [3] R. G. E. Murray moved with his family in 1930 to Montreal.