Maximal independent sets on a grid graph
نویسندگان
چکیده
منابع مشابه
MAXIMAL INDEPENDENT SETS FOR THE PIXEL EXPANSION OF GRAPH ACCESS STRUCTURE
Given a graph G, a visual cryptography scheme based on the graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper we apply maximal independent sets of the grap...
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Let G be a (simple, undirected, finite) graph. A set S ⊆ V (G) is independent if no edge of G has both its endpoints in S. An independent set S is maximal if no independent set of G properly contains S. Let MIS(G) be the set of all maximal independent sets in G. Miller and Muller (1960) and Moon and Moser (1965) independently proved that the maximum, taken over all n-vertex graphs G, of |MIS(G)...
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Abstract : A visual cryptography scheme based on a given graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper a maximal independent sets of the graph G was ...
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A caterpillar graph is a tree which on removal of all its pendant vertices leaves a chordless path. The chordless path is called the backbone of the graph. The edges from the backbone to the pendant vertices are called the hairs of the caterpillar graph. Ortiz and Villanueva (C.Ortiz and M.Villanueva, Discrete Applied Mathematics, 160(3): 259-266, 2012) describe an algorithm, linear in the size...
متن کاملThe Number of Independent Sets in a Grid Graph
Let Gm,n be the m×n grid graph. That is, the vertices of Gm,n are the (m+1)(n+1) points (i, j) (0 ≤ i ≤ m, 0 ≤ j ≤ n) in the plane, and its edges are all of the pairs (i, j), (i′, j′) of vertices for which |i − i′| + |j − j′| = 1. Let f(m,n) be the number of independent sets of vertices in Gm,n. We study the growth of f(m,n). The figure below shows an independent set S in G4,6. figure=grid.eps ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.08.015