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A size chart illustrating the ANSI sizes. In 1992, the American National Standards Institute adopted ANSI/ASME Y14.1 Decimal Inch Drawing Sheet Size and Format, [1] which defined a regular series of paper sizes based upon the de facto standard 8 + 1 ⁄ 2 in × 11 in "letter" size to which it assigned the designation "ANSI A".
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In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes . For example, a square vertex arrangement is understood to mean four points in a plane, equal distance and angles from a center point.
For a graph = (,), an independent set is a maximal independent set if for , one of the following is true: [1] where () denotes the neighbors of The above can be restated as a vertex either belongs to the independent set or has at least one neighbor vertex that belongs to the independent set.
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A vertex coloring of a graph corresponds to a partition of its vertex set into independent subsets. Hence the minimal number of colors needed in a vertex coloring, the chromatic number χ ( G ) {\displaystyle \chi (G)} , is at least the quotient of the number of vertices in G {\displaystyle G} and the independent number α ( G ) {\displaystyle ...
The vertex-connectivity of an input graph G can be computed in polynomial time in the following way [4] consider all possible pairs (,) of nonadjacent nodes to disconnect, using Menger's theorem to justify that the minimal-size separator for (,) is the number of pairwise vertex-independent paths between them, encode the input by doubling each vertex as an edge to reduce to a computation of the ...
Petersen graph as Kneser graph ,. The Petersen graph is the complement of the line graph of .It is also the Kneser graph,; this means that it has one vertex for each 2-element subset of a 5-element set, and two vertices are connected by an edge if and only if the corresponding 2-element subsets are disjoint from each other.