Some Remarks on Α-domination
نویسندگان
چکیده
Let α ∈ (0, 1) and let G = (VG, EG) be a graph. According to Dunbar, Hoffman, Laskar and Markus [3] a set D ⊆ VG is called an α-dominating set of G, if |NG(u)∩D| ≥ αdG(u) for all u ∈ VG \D. We prove a series of upper bounds on the α-domination number of a graph G defined as the minimum cardinality of an α-dominating set of G.
منابع مشابه
Two Remarks on the Domination Number of Graphs
This paper consists of two loosely related notes on the domination number of graphs. In the first part, we provide a new upper bound for the domination number of d-regular graphs. Our bound is the best known for d ≥ 6. In the second part, we compute the exact domination number and total domination number of certain Kneser graphs, and we provide some bounds on the domination number of other Knes...
متن کاملComplexity results for $k$-domination and $\alpha$-domination problems and their variants
Let G = (V,E) be a simple and undirected graph. For some integer k > 1, a set D ⊆ V is said to be a k-dominating set in G if every vertex v of G outside D has at least k neighbors in D. Furthermore, for some real number α with 0 < α 6 1, a set D ⊆ V is called an α-dominating set in G if every vertex v of G outside D has at least α×dv neighbors in D, where dv is the degree of v in G. The cardina...
متن کاملSome results of domination and total domination in the direct product of two fuzzy graphs
In this article we give a new definition of direct product of two arbitrary fuzzy graphs. We define the concepts of domination and total domination in this new product graph. We obtain an upper bound for the total domination number of the product fuzzy graph. Further we define the concept of total α-domination number and derive a lower bound for the total domination number of the product fuzzy ...
متن کاملOn the total domination subdivision number in graphs
A set S ⊆ V of vertices in a graph G = (V,E) without isolated vertices is a total dominating set if every vertex of V is adjacent to some vertex in S. The total domination number γt(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in...
متن کاملNon Split Domination on Intuitionistic Fuzzy Graphs
A dominating set D of an IFG G = (V, E) is a non-split dominating set, if the induced intuitionistic fuzzy subgraph 〈ܸ − 〉ܦ is connected. The Non-split domination number ߛ ௦ ሺܩሻ of IFG G is the minimum cardinality of all Non-split dominating set. In this paper we study some theorems in Non-split dominating sets of IFG and some results of ߛ ௦ ሺܩሻwith other known parameters of IFG G. 1. In...
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:
دوره شماره
صفحات -
تاریخ انتشار 2004