Domination Parameters of Hypercubes and Star Graphs
ثبت نشده
چکیده
In this chapter, we investigate the properties of domination parameters of Hypercubes and star graphs. For Hypercubes Q, we prove that if n = 1, then (Q) = = = n—k We also prove that -y(Q) = 7, y(Q) = 12, y(Q) = 16 and 'y(Q) 2 for all n 7. We determine the values of 'yj, Yt, 'Ye and yp for Qn where n 6 and obtain bounds for these parameters for n > 7. For n-star graph S we determine the values of 'y, 'y, 'yp and obtain bounds for 'Yt and 7c
منابع مشابه
Domination parameters of Cayley graphs of some groups
In this paper, we investigate domination number, $gamma$, as well as signed domination number, $gamma_{_S}$, of all cubic Cayley graphs of cyclic and quaternion groups. In addition, we show that the domination and signed domination numbers of cubic graphs depend on each other.
متن کاملA Note on “on The Power Dominating Sets of Hypercubes”
1. Any vertex that is incident to an observed edge is observed. 2. Any edge joining two observed vertices is observed. The power domination problem is a variant of the classical domination problem in graphs and is defined as follows. Given an undirected graph G = (V, E), the problem is to find a minimum vertex set SP ⊆ V , called the power dominating set of G, such that all vertices in G are ob...
متن کاملTotal double Roman domination in graphs
Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:Vrightarrow{0,1,2,3}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one vertex assigned $3$ under $f$, whereas if $f(v)=1$, then the vertex $v$ must be adjacent to at least one vertex assigned $2$ or $3$. The weight of a DR...
متن کاملSelf-diagnosability Results and Diagnosis Algorithms for Hypercubes and Star Graphs
Our purpose in the present paper is to do a detailed investigation of the diierent aspects of t-diagnosability and t=t-diagnosability of hypercubes and star graphs. We compute that the degree of diagnosability of a star graph S n is 2n ? 4 (that of a hypercube is 2n ? 2 4]). We then propose a simple yet eecient algorithm to locate faults in hypercubes and star graphs under both t-diagnosis and ...
متن کاملLeader election in oriented star graphs
Leader election in a network plays an important role in the area of distributed algorithm design. Structural properties of the network as well as presence of direction on the edges of the network greatly affects the complexity of the leader election problem which is primarily measure by the message complexity of the protocol. Our purpose in the present paper is to adapt the existing distributed...
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 2015