Upper bounds for the k-subdomination number of graphs
نویسندگان
چکیده
منابع مشابه
Upper bounds for the k-subdomination number of graphs
For a positive integer k, a k-subdominating function of G=(V; E) is a function f :V → {−1; 1} such that the sum of the function values, taken over closed neighborhoods of vertices, is at least one for at least k vertices of G. The sum of the function values taken over all vertices is called the aggregate of f and the minimum aggregate among all k-subdominating functions of G is the k-subdominat...
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For a set of non-negative integers~$L$, the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots, l}$ to vertices $v$, such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...
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For a positive integer k, a k-subdominating function of a graph G=(V; E) is a function f :V →{−1; 1} such that ∑u∈NG [v] f(u)¿ 1 for at least k vertices v of G. The ksubdomination number of G, denoted by ks(G), is the minimum of ∑ v∈V f(v) taken over all k-subdominating functions f of G. In this article, we prove a conjecture for k-subdomination on trees proposed by Cockayne and Mynhardt. We al...
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Let G be a graph with vertex set V (G), and let f : V (G) −→ {−1, 1} be a two-valued function. If k ≥ 1 is an integer and ∑ x∈N(v) f(x) ≥ k for each v ∈ V (G), where N(v) is the neighborhood of v, then f is a signed total k-dominating function on G. A set {f1, f2, . . . , fd} of distinct signed total k-dominating functions on G with the property that ∑d i=1 fi(x) ≤ k for each x ∈ V (G), is call...
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The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and of all edges having a common end-vertex with e. Let f be a function on E(G), the edge set of G, into the set {−1, 0, 1}. If ∑ x∈N [e] f(x) ≥ 1 for at least k edges e of G, then f is called a minus edge k-subdominating function of G. The minimum of the values ∑ e∈E(G) f(e), taken over all minus edge k-subdomin...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00311-9