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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).
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
[2] [3] Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics , most notably in Euclid 's Elements . [ 4 ] Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions ), until the 16th and 17th centuries, when ...
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.
According to Brooks' theorem every connected cubic graph other than the complete graph K 4 has a vertex coloring with at most three colors. Therefore, every connected cubic graph other than K 4 has an independent set of at least n/3 vertices, where n is the number of vertices in the graph: for instance, the largest color class in a 3-coloring has at least this many vertices.
Mobile learning can provide performance support for checking the time, setting reminders, retrieving worksheets, and instruction manuals. [ 118 ] [ 119 ] Such devices as iPads are used for helping disabled (visually impaired or with multiple disabilities) children in communication development as well as in improving physiological activity ...
Education in Cuba has been a highly ranked system for many years. The University of Havana was founded in 1727 and there are a number of other well-established colleges and universities . Following the 1959 revolution, the Castro government nationalized all educational institutions, and created a government operated system.
Taíno genocide Viceroyalty of New Spain (1535–1821) Siege of Havana (1762) Captaincy General of Cuba (1607–1898) Lopez Expedition (1850–1851) Ten Years' War (1868–1878) Little War (1879–1880) Cuban War of Independence (1895–1898) Treaty of Paris (1898) US Military Government (1898–1902) Platt Amendment (1901) Republic of Cuba (1902–1959) Cuban Pacification (1906–1909) Negro ...