منابع مشابه
Incidence dominating numbers of graphs
In this paper, the concept of incidence domination number of graphs is introduced and the incidence dominating set and the incidence domination number of some particular graphs such as paths, cycles, wheels, complete graphs and stars are studied.
متن کاملThe k-dominating cycles in graphs
For a graph G, let σ̄k+3(G) = min {d(x1) + d(x2) + · · · + d(xk+3) − |N(x1) ∩ N(x2) ∩ · · · ∩ N(xk+3)| | x1, x2, · · · , xk+3 are k + 3 independent vertices in G}. In [5], H. Li proved that if G is a 3-connected graph of order n and σ̄4(G) ≥ n+3, then G has a maximum cycle such that each component of G−C has at most one vertex. In this paper, we extend this result as follows. Let G be a (k + 2)-c...
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Minimum m-connected k-dominating set problem is as follows: Given a graph G= (V ,E) and two natural numbers m and k, find a subset S ⊆ V of minimal size such that every vertex in V \ S is adjacent to at least k vertices in S and the induced graph of S is m-connected. In this paper we study this problem with unit disc graphs and small m, which is motivated by the design of fault-tolerant virtual...
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We show that interval graphs on n vertices have at most 3 ≈ 1.4422 minimal dominating sets, and that these can be enumerated in time O∗(3n/3). As there are examples of interval graphs that actually have 3 minimal dominating sets, our bound is tight. We show that the same upper bound holds also for trees, i.e. trees on n vertices have at most 3 ≈ 1.4422 minimal dominating sets. The previous best...
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In Graph Theory, independent number and, dominating number are three of the important parameters to measure the resilience of graphs, respectively denoted by ( ) G and ( ) G for a graph G . But predecessors have proved that computing them are very hard. So computing ( ) G and ( ) G of some particular known graphs is extremely valuable. In this paper, we determine ( ) G and ( ) G of ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.10.013