منابع مشابه
Domination Reliability
In this paper, we propose a new network reliability measure for some particular kind of service networks, which we refer to as domination reliability. We relate this new reliability measure to the domination polynomial of a graph and the coverage probability of a hypergraph. We derive explicit and recursive formulæ for domination reliability and its associated domination reliability polynomial,...
متن کاملHypo-efficient domination and hypo-unique domination
For a graph $G$ let $gamma (G)$ be its domination number. We define a graph G to be (i) a hypo-efficient domination graph (or a hypo-$mathcal{ED}$ graph) if $G$ has no efficient dominating set (EDS) but every graph formed by removing a single vertex from $G$ has at least one EDS, and (ii) a hypo-unique domination graph (a hypo-$mathcal{UD}$ graph) if $G$ has at least two minimum dominating sets...
متن کاملInequalities Involving Independence Domination , / - Domination , Connected and Total / - Domination Numbers
Let / be an integer-valued function defined on the vertex set V(G) of a graph G. A subset D of V(G) is an /-dominating set if each vertex x outside D is adjacent to at least f(x) vertices in D. The minimum number of vertices in an /-dominating set is denned to be the /-domination number, denoted by 7/(G). In a similar way one can define the connected and total /-domination numbers 7 C| /(G) and...
متن کاملTotal domination versus paired domination
A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by γt. The maximal size of an inclusionwise minimal total dominating set, the upper total domination num...
متن کاملComplexity of Comparing the Domination Number to the Independent Domination, Connected Domination, and Paired Domination Numbers
The domination number γ(G), the independent domination number ι(G), the connected domination number γc(G), and the paired domination number γp(G) of a graph G (without isolated vertices, if necessary) are related by the simple inequalities γ(G) ≤ ι(G), γ(G) ≤ γc(G), and γ(G) ≤ γp(G). Very little is known about the graphs that satisfy one of these inequalities with equality. I.E. Zverovich and V...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/1166