The Modified Negative Decision Number in Graphs
نویسندگان
چکیده
منابع مشابه
The Modified Negative Decision Number in Graphs
A mapping x : V → {−1, 1} is called negative if∑u∈N v x u ≤ 1 for every v ∈ V. The maximum of the values of ∑ v∈V x v taken over all negative mappings x, is called the modified negative decision number and is denoted by β′ D G . In this paper, several sharp upper bounds of this number for a general graph are presented. Exact values of these numbers for cycles, paths, cliques and bicliques are f...
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A bad function is a function f : V (G) → {−1, 1} satisfying ∑ v∈N(v) f(v) ≤ 1 for every v ∈ V (G), where N(v) = {u ∈ V (G) | uv ∈ E(G)}. The maximum of the values of ∑ v∈V (G) f(v), taken over all bad functions f, is called the negative decision number and is denoted by βD(G). In this paper, several sharp upper bounds of this number for general graphs are presented.
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Let G = (V,E) be a graph. A function f : V → {−1, 1} is called a bad function of G if ∑ u∈NG(v) f(u) ≤ 1 for each v ∈ V , where NG(v) is the set of neighbors of v in G. The negative decision number of G, introduced by Wang, is the maximum value of ∑ v∈V f(v) taken over all bad functions of G. In this paper, we comprehensively study the negative decision number from algorithmic, complexity, and ...
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Let G = (V,E) be a graph. A function f : V → {−1, 1} is called a bad function of G if ∑ u∈NG(v) f(u) ≤ 1 for all v ∈ V , where NG(v) denotes the set of neighbors of v in G. The negative decision number of G, introduced in [12], is the maximum value of ∑ v∈V f(v) taken over all bad functions of G. In this paper, we present sharp upper bounds on the negative decision number of a graph in terms of...
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Let G be a graph. A good function is a function f : V (G)→ {−1, 1}, satisfying f(N(v)) ≥ 1, for each v ∈ V (G), where N(v) = {u ∈ V (G) |uv ∈ E(G)} and f(S) = ∑ u∈S f(u) for every S ⊆ V (G). For every cubic graph G of order n, we prove that γ(G) ≤ 5n 7 and show that this inequality is sharp. A function f : V (G) → {−1, 1} is called a nice function, if f(N [v]) ≤ 1, for each v ∈ V (G), where N [...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2011
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2011/135481