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In mathematics, an empty sum, or nullary sum, [1] is a summation where the number of terms is zero. The natural way to extend non-empty sums [ 2 ] is to let the empty sum be the additive identity . Let a 1 {\displaystyle a_{1}} , a 2 {\displaystyle a_{2}} , a 3 {\displaystyle a_{3}} , ... be a sequence of numbers, and let
The criterion of minimalization is the sum of colors Star coloring Every 2-chromatic subgraph is a disjoint collection of stars Strong coloring Every color appears in every partition of equal size exactly once Strong edge coloring Edges are colored such that each color class induces a matching (equivalent to coloring the square of the line graph)
The sum of the labels is 11, smaller than could be achieved using only two labels. In graph theory, a sum coloring of a graph is a labeling of its vertices by positive integers, with no two adjacent vertices having equal labels, that minimizes the sum of the labels. The minimum sum that can be achieved is called the chromatic sum of the graph. [1]
Killer sudoku (also killer su doku, sumdoku, sum doku, sumoku, addoku, or samunanpure サムナンプレ sum-num(ber) pla(ce)) is a puzzle that combines elements of sudoku and kakuro. Despite the name, the simpler killer sudokus can be easier to solve than regular sudokus, depending on the solver's skill at mental arithmetic ; the hardest ones ...
A root (or zero) of a chromatic polynomial, called a “chromatic root”, is a value x where (,) =. Chromatic roots have been very well studied, in fact, Birkhoff’s original motivation for defining the chromatic polynomial was to show that for planar graphs, P ( G , x ) > 0 {\displaystyle P(G,x)>0} for x ≥ 4.
The summation of an explicit sequence is denoted as a succession of additions. For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands ...
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Version 0.46 of Inkscape includes a bucket fill tool, giving output similar to ordinary bitmap operations and indeed using one: the canvas is rendered, a flood fill operation is performed on the selected area and the result is then traced back to a path.