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Horner's method can be used to convert between different positional numeral systems – in which case x is the base of the number system, and the a i coefficients are the digits of the base-x representation of a given number – and can also be used if x is a matrix, in which case the gain in computational efficiency is even greater.
name vertices edges radius diam. girth P χ χ' 120-cell: 600: 1200: 15: 15: 5: F: 3: 4 Balaban 3-10-cage: 70: 105: 6: 6: 10: F: 2: 3 Balaban 3-11-cage: 112: 168: 6 ...
For example, antiderivatives of x 2 + 1 have the form 1 / 3 x 3 + x + c. For polynomials whose coefficients come from more abstract settings (for example, if the coefficients are integers modulo some prime number p , or elements of an arbitrary ring), the formula for the derivative can still be interpreted formally, with the coefficient ...
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.
The Errera graph is planar and has chromatic number 4, chromatic index 6, radius 3, diameter 4 and girth 3. All its vertices are of degree 5 or 6 and it is a 5-vertex-connected graph and a 5-edge-connected graph. The Errera graph is not a vertex-transitive graph and its full automorphism group is isomorphic to the dihedral group of order 20 ...
Therefore, the graph of the function f(x − h) = (x − h) 2 is a parabola shifted to the right by h whose vertex is at (h, 0), as shown in the top figure. In contrast, the graph of the function f(x) + k = x 2 + k is a parabola shifted upward by k whose vertex is at (0, k), as shown in the center figure.
All non-isomorphic graphs on 3 vertices and their chromatic polynomials, clockwise from the top. The independent 3-set: k 3. An edge and a single vertex: k 2 (k – 1). The 3-path: k(k – 1) 2. The 3-clique: k(k – 1)(k – 2). The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics.
The Shrikhande graph shares these parameters with exactly one other graph, the 4×4 rook's graph, i.e., the line graph L(K 4,4) of the complete bipartite graph K 4,4. The latter graph is the only line graph L(K n,n) for which the strong regularity parameters do not determine that graph uniquely but are shared with a different graph, namely the ...