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The 1st Earl of Bolingbroke, a seventeenth-century English aristocrat and politician. Aristocracy (from Ancient Greek ἀριστοκρατίᾱ ( aristokratíā ) 'rule of the best'; from ἄριστος ( áristos ) 'best' and κράτος ( krátos ) 'power, strength') is a form of government that places power in the hands of a small ...
The complete bipartite graph K m,n has a vertex covering number of min{m, n} and an edge covering number of max{m, n}. The complete bipartite graph K m,n has a maximum independent set of size max{m, n}. The adjacency matrix of a complete bipartite graph K m,n has eigenvalues √ nm, − √ nm and 0; with multiplicity 1, 1 and n + m − 2 ...
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Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring ...
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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.
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.