On signed edge domination numbers of trees
نویسندگان
چکیده
منابع مشابه
On Signed Edge Domination Numbers of Trees
The signed edge domination number of a graph is an edge variant of the signed domination number. The closed neighbourhood 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 mapping of the edge set E(G) of G into the set {−1, 1}. If ∑ x∈N [e] f(x) 1 for each e ∈ E(G), then f is called a signed edge dominating function on G. T...
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The open neighborhood NG(e) of an edge e in a graph G is the set consisting of all edges having a common end-vertex with e and its closed neighborhood is NG[e] = NG(e) ∪ {e}. Let f be a function on E(G), the edge set of G, into the set {−1, 1}. If ∑x∈NG[e] f(x) ≥ 1 for at least a half of the edges e ∈ E(G), then f is called a signed edge majority dominating function of G. The minimum of the val...
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For the terminology and notations not defined here, we adopt those in Bondy and Murty [1] and Xu [2] and consider simple graphs only. Let G = (V,E) be a graph with vertex set V = V (G) and edge set E = E(G). For any vertex v ∈ V , NG(v) denotes the open neighborhood of v in G and NG[v] = NG(v) ∪ {v} the closed one. dG(v) = |NG(v)| is called the degree of v in G, ∆ and δ denote the maximum degre...
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Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simplegraph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph$G$ is the set consisting of $e$ and all edges having a commonend-vertex with $e$. A signed Roman edge $k$-dominating function(SREkDF) on a graph $G$ is a function $f:E rightarrow{-1,1,2}$ satisfying the conditions that (i) for every edge $e$of $G$, $sum _{xin N[e]} f...
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In this paper, we study both concepts of geodetic dominatingand edge geodetic dominating sets and derive some tight upper bounds onthe edge geodetic and the edge geodetic domination numbers. We also obtainattainable upper bounds on the maximum number of elements in a partitionof a vertex set of a connected graph into geodetic sets, edge geodetic sets,geodetic domin...
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 2002
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2002.133984