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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]
Labels like red and blue are only used when the number of colors is small, and normally it is understood that the labels are drawn from the integers {1, 2, 3, ...}. A coloring using at most k colors is called a (proper) k-coloring. The smallest number of colors needed to color a graph G is called its chromatic number, and is often denoted χ(G).
The American Society of Cinematographers (ASC) defines lighting ratio as (key+fill):fill, or (key+Σ fill):Σ fill, where Σ fill is the sum of all fill lights. Light can be measured in footcandles. A key light of 200 footcandles and fill light of 100 footcandles have a 3:1 ratio (a ratio of three to one) — (200 + 100):100.
When one of the components has the strongest intensity, the color is a hue near this primary color (red-ish, green-ish, or blue-ish), and when two components have the same strongest intensity, then the color is a hue of a secondary color (a shade of cyan, magenta, or yellow). A secondary color is formed by the sum of two primary colors of equal ...
George David Birkhoff introduced the chromatic polynomial in 1912, defining it only for planar graphs, in an attempt to prove the four color theorem.If (,) denotes the number of proper colorings of G with k colors then one could establish the four color theorem by showing (,) > for all planar graphs G.
The equitable chromatic number of a graph G is the smallest number k such that G has an equitable coloring with k colors. But G might not have equitable colorings for some larger numbers of colors; the equitable chromatic threshold of G is the smallest k such that G has equitable colorings for any number of colors greater than or equal to k. [2]
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Rooted in their interconnecting relationship with the golden ratio is the notion that the sum of third consecutive Fibonacci numbers equals a Lucas number, that is = + + ; and, importantly, that = / .