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The cube of every connected graph necessarily contains a Hamiltonian cycle. [10] It is not necessarily the case that the square of a connected graph is Hamiltonian, and it is NP-complete to determine whether the square is Hamiltonian. [11] Nevertheless, by Fleischner's theorem, the square of a 2-vertex-connected graph is always Hamiltonian. [12]
Two to the power of n, written as 2 n, is the number of values in which the bits in a binary word of length n can be set, where each bit is either of two values. A word, interpreted as representing an integer in a range starting at zero, referred to as an "unsigned integer", can represent values from 0 (000...000 2) to 2 n − 1 (111...111 2) inclusively.
The binary number system expresses any number as a sum of powers of 2, and denotes it as a sequence of 0 and 1, separated by a binary point, where 1 indicates a power of 2 that appears in the sum; the exponent is determined by the place of this 1: the nonnegative exponents are the rank of the 1 on the left of the point (starting from 0), and ...
A comparison of the linear and quadratic approximations (in red and blue respectively) of the function , from x = −2 to x = 2 Beyond linear approximations, a quadratic approximation (to the differentiability requirement) is given by:
Global warming is primarily a result of the increase in atmospheric greenhouse-gas concentrations (like CO 2 and methane) via the burning of fossil fuels as well as other human activities such as deforestation, with secondary climate change feedback mechanisms (such as the melting of the polar ice increasing the Earth's absorption of sunlight ...
The blaze tore through the first floor of a six-story building West 204th Street building in Inwood starting about 8:25 a.m., the FDNY said. A fire in NYC left 15 injured Citizen.
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y = a x k {\displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the exponent corresponding to ...
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