نتایج جستجو برای: ‎irredundance number‎

تعداد نتایج: 1168378  

Journal: :Journal of Graph Theory 2002
Lutz Volkmann Vadim E. Zverovich

Let ir(G) and γ(G) be the irredundance number and the domination number of a graph G, respectively. A graph G is called irredundance perfect if ir(H) = γ(H), for every induced subgraph H of G. In this article we present a result which immediately implies three known conjectures on irredundance perfect graphs.

Journal: :bulletin of the iranian mathematical society 0
h. hosseinzadeh department of mathematics‎, ‎alzahra university‎, ‎p.o. box 19834, tehran‎, ‎iran. n. soltankhah department of mathematics‎, ‎alzahra university‎, ‎p.o. box 19834, tehran‎, ‎iran.

‎let $g=(v(g),e(g))$ be a graph‎, ‎$gamma_t(g)$. let $ooir(g)$ be the total domination and oo-irredundance number of $g$‎, ‎respectively‎. ‎a total dominating set $s$ of $g$ is called a $textit{total perfect code}$ if every vertex in $v(g)$ is adjacent to exactly one vertex of $s$‎. ‎in this paper‎, ‎we show that if $g$ has a total perfect code‎, ‎then $gamma_t(g)=ooir(g)$‎. ‎as a consequence, ...

Journal: :Discrete Mathematics 2002
Lutz Volkmann Vadim E. Zverovich

Let ir(G) and γ(G) be the irredundance number and the domination number of a graph G, respectively. A graph G is called irredundance perfect if ir(H) = γ(H), for every induced subgraph H of G. In this paper we disprove the known conjecture of Henning [3, 11] that a graph G is irredundance perfect if and only if ir(H) = γ(H) for every induced subgraph H of G with ir(H) ≤ 4. We also give a summar...

2008
S. Arumugam M. Subramanian

The six basic parameters relating to domination, independence and irredundance satisfy a chain of inequalities given by ir ≤ γ ≤ i ≤ β0 ≤ Γ ≤ IR where ir, IR are the irredundance and upper irredundance numbers, γ,Γ are the domination and upper domination numbers and i, β0 are the independent domination number and independence number respectively. In this paper, we introduce the concept of indep...

Journal: :Australasian J. Combinatorics 1998
Ernest J. Cockayne Odile Favaron Joël Puech Christina M. Mynhardt

A variety of relationships between graph parameters involving packings, perfect neighbourhood, irredundant and R-annihilated sets is obtained. Some of the inequalities are improvements of existing bounds for the lower irredundance number, and others are motivated by the conjecture (recently disproved) that for any graph the smallest cardinality of a perfect neighbourhood set is at most the lowe...

2006
Dongdong Wang Hongbo Hua

A vertex v in a vertex-subset I of an undirected graph G is said to be redundant if its closed neighborhood is contained in the union of closed neighborhoods of vertices of I − {v}. In the context of a communication network , this means that any vertex that may receive communications from I may also be informed from I − {v} . The irredundance number ir(G) is the minimum cardinality taken over a...

Journal: :Discussiones Mathematicae Graph Theory 2014
Changiz Eslahchi Shahab Haghi Nader Jafari Rad

A subset S of vertices in a graph G is called a total irredundant set if, for each vertex v in G, v or one of its neighbors has no neighbor in S − {v}. The total irredundance number, ir(G), is the minimum cardinality of a maximal total irredundant set of G, while the upper total irredundance number, IR(G), is the maximum cardinality of a such set. In this paper we characterize all cubic graphs ...

Journal: :Graphs and Combinatorics 2005
Igor E. Zverovich Vadim E. Zverovich

Let ir(G), γ(G), i(G), β0(G), Γ(G) and IR(G) be the irredundance number, the domination number, the independent domination number, the independence number, the upper domination number and the upper irredundance number of a graph G, respectively. In this paper we show that for any integers k1, k2, k3, k4, k5 there exists a cubic graph G satisfying the following conditions: γ(G)−ir(G) ≥ k1, i(G)−...

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