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The degree sum formula states that, given a graph = (,), = | |. The formula implies that in any undirected graph, the number of vertices with odd degree is even. This statement (as well as the degree sum formula) is known as the handshaking lemma. The latter name comes from a popular mathematical problem, which is to prove that in any group ...
Alternatively, it is possible to use mathematical induction to prove the degree sum formula, [2] or to prove directly that the number of odd-degree vertices is even, by removing one edge at a time from a given graph and using a case analysis on the degrees of its endpoints to determine the effect of this removal on the parity of the number of ...
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer .
Because the degree of a non-zero polynomial is the largest degree of any one term, this polynomial has degree two. [ 11 ] Two terms with the same indeterminates raised to the same powers are called "similar terms" or "like terms", and they can be combined, using the distributive law , into a single term whose coefficient is the sum of the ...
Vieta's formulas can equivalently be written as < < < (=) = for k = 1, 2, ..., n (the indices i k are sorted in increasing order to ensure each product of k roots is used exactly once). The left-hand sides of Vieta's formulas are the elementary symmetric polynomials of the roots.
Partition function: Order-independent count of ways to write a given positive integer as a sum of positive integers. Möbius μ function: Sum of the nth primitive roots of unity, it depends on the prime factorization of n. Prime omega functions; Chebyshev functions; Liouville function, λ(n) = (–1) Ω(n)
In mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by the same scalar, then the function's value is multiplied by some power of this scalar; the power is called the degree of homogeneity, or simply the degree.
In mathematics, Newton's identities ... (that is, the sum of all monomials of degree ... As a telescopic sum of symmetric function identities