Relating the annihilation number and the total domination number of a tree
نویسندگان
چکیده
منابع مشابه
Relating the annihilation number and the 2-domination number of a tree
A set S of vertices in a graph G is a 2-dominating set if every vertex of G not in S is adjacent to at least two vertices in S. The 2-domination number γ2(G) is the minimum cardinality of a 2-dominating set in G. The annihilation number a(G) is the largest integer k such that the sum of the first k terms of the nondecreasing degree sequence of G is at most the number of edges in G. The conjectu...
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a {em 2-rainbow dominating function} (2rdf) of a graph $g$ is a function $f$ from the vertex set $v(g)$ to the set of all subsets of the set ${1,2}$ such that for any vertex $vin v(g)$ with $f(v)=emptyset$ the condition $bigcup_{uin n(v)}f(u)={1,2}$ is fulfilled, where $n(v)$ is the open neighborhood of $v$. the {em weight} of a 2rdf $f$ is the value $omega(f)=sum_{vin v}|f (v)|$. the {em $2$-r...
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a set $s$ of vertices in a graph $g$ is a dominating set if every vertex of $v-s$ is adjacent to some vertex in $s$. the domination number $gamma(g)$ is the minimum cardinality of a dominating set in $g$. the annihilation number $a(g)$ is the largest integer $k$ such that the sum of the first $k$ terms of the non-decreasing degree sequence of $g$ is at most the number of edges in $g$. in this p...
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A edge 2-rainbow dominating function (E2RDF) of a graph G is a function f from the edge set E(G) to the set of all subsets of the set {1,2} such that for any edge.......................
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A set S of vertices in a graph G is a dominating set if every vertex of V − S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set in G. The annihilation number a(G) is the largest integer k such that the sum of the first k terms of the non-decreasing degree sequence of G is at most the number of edges in G. In this paper, we show that for a...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.09.006