# independence number

## independence number

[‚in·di′pen·dəns ‚nəm·bər]
(mathematics)
For a graph, the largest possible number of vertices in an independent set. Also known as internal stability number.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Since independence number of Radio stations has steadily registered increase.
A set of rectangles is said to be independent if they are pairwise independent, and we define the independence number of a set of axis-parallel rectangles to be the size of the largest independent set of rectangles it contains.
It follows readily that if [Real part] is a set of closed axis-parallel rectangles and [Imaginary part] is the corresponding set of 2-intervals then the independence number of [Real part] is equal to the packing number of [Imaginary part].
will take significantly The 2015 UK general election factor in be a complicating negotiations, if the Labour Party independence number of secure a substantial seats in Scotland but fail to win or outright majority commanding in the House of Commons.
 studied the various lower and upper bounds for the EDS in terms of other graph invariants including the Wiener index, the degree distance, the eccentric connectivity index, independence number, connectivity, matching number, chromatic number, and clique number.
The independence number is the size of a maximum independent set in a graph and is denoted by [alpha](G).
Thus the independence number of SR(d, n) is the maximum number of nonattacking rooks that can be placed on a simplicial chessboard with n + 1 "squares" on each side.
The independence number of SR(d, n) can be interpreted as the maximum number of nonattacking "rooks" that can be placed on a simplicial chessboard of side length n + 1.
The independence number and edge independence number of G are respectively denoted by [[beta].sub.0] and [[beta].sub.1].
There is a vast amount of literature concerning conditions in terms of for instance order, size, vertex degrees, degree sums, independence number, chromatic number, feedback vertex sets that are sufficient for the existence of some number of vertex-disjoint cycles, which may additionally contain specified elements or satisfy certain length conditions.
It should be noted that if G is triangle-free, then a set is a clique-transversal set of G if and only if it meets all edges--i.e., it is a vertex cover--therefore [[tau].sub.c](G) is equal to the number of vertices minus the independence number of G in this case.
Graph coloring and related topics of cliques, independence numbers, and graph factorization are addressed next.

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