Fractional domination in prisms
نویسنده
چکیده
Mynhardt has conjectured that if G is a graph such that γ(G) = γ(πG) for all generalized prisms πG then G is edgeless. The fractional analogue of this conjecture is established and proved by showing that, if G is a graph with edges, then γf (G×K2) > γf (G).
منابع مشابه
Domination number of graph fractional powers
For any $k in mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by ...
متن کاملRoman domination in complementary prisms
The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect matching between the corresponding vertices of G and G. A Roman dominating function on a graph G = (V,E) is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 is adjacent to a vertex with label 2. The Roman domination number γR(G) ofG is the mini...
متن کاملPaired domination in prisms of graphs
The paired domination number γpr(G) of a graph G is the smallest cardinality of a dominating set S of G such that 〈S〉 has a perfect matching. The generalized prisms πG of G are the graphs obtained by joining the vertices of two disjoint copies of G by |V (G)| independent edges. We provide characterizations of the following three classes of graphs: γpr(πG) = 2γpr(G) for all πG; γpr(K2 G) = 2γpr(...
متن کاملBalancedness and Concavity of Fractional Domination Games
In this paper, we introduce a fractional domination game arising from fractional domination problems on graphs and focus on its balancedness and concavity. We first characterize the core of the fractional domination game and show that its core is always non-empty taking use of dual theory of linear programming. Furthermore we study concavity of this game.
متن کاملMinimum fractional dominating functions and maximum fractional packing functions
The fractional analogues of domination and packing in a graph form an interesting pair of dual linear programs in that the feasible vectors for both LPs have interpretations as functions from the vertices of the graph to the unit interval; efficient (fractional) domination is accomplished when a function simultaneously solves both LPs. We investigate some structural properties of the functions ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 27 شماره
صفحات -
تاریخ انتشار 2007