[PDF] Top 20 A Review on Graphs with Unique Minimum Dominating Sets

... areas. Graphs are also used to represent the micro-scale channels of porous media, in which the vertices represent the pores and the edges represent the smaller channels connecting the ... See full document

... strong dominating set if D is a strong dominating set and χ(< D >) = ...The minimum cardinality of a chromatic strong dominating set is called the chromatic strong domination number of G ... See full document

... Fuzzy graphs were introduced by Rosenfeld ...fuzzy graphs and chromatic number of fuzzy graphs were discussed in ...fuzzy graphs was also done by Akram, Samanta, Nayeem, Pramanik, Rashmanlou ... See full document

... in graphs was begun by Ore and ...A dominating set of a graph G is a set D of vertices of G such that every vertex in V–D is adjacent to atleast one vertex in D and the minimum cardinality among all ... See full document

... All graphs considered in this work will be finite, simple, and contain no isolated ...a dominating set (or just dominating, for short) if for each vertex v 6∈ D, v is adjacent to some vertex of ...a ... See full document

... connected dominating set, if is a dominating set and the sub graph is triple ...The minimum cardinality taken over all triple connected dominating sets of is called the triple connected ... See full document

... We now show that is minimum. Suppose we delete a vertex, say from . Then the vertices and are not dominated by the remaining vertex This is because and is not adjacent with as . Similar is the case if we delete ... See full document

... By a graph G = (V, E) we mean a finite undirected graph without loops or multiple edges. The order and size of G are denoted by p and q respectively. For graph theoretical terms, we refer to Harary [2] and for terms ... See full document

... minimal dominating set is formed in any other way, then the cardinality of such a set is not smaller than that of This follows from the properties of the prime divisors of a ...strong dominating set of with ... See full document

... convex dominating set 𝑆 in a connected graph 𝐺 is a secure restrained convex dominating set, if for each element 𝑢 in 𝑉(𝐺)\𝑆 there exists an element 𝑣 in 𝑆 such that 𝑢𝑣 ∈ 𝐸(𝐺) and (𝑆 \{ 𝑣 }) ∪ { 𝑢 } is a ... See full document

... The Fuzzy Directed Graph, Fuzzy competition digraphs are well known topic.The concept of domination in fuzzy graphs are introduced by A. Somasundaram and S. Somasundaram [] in 1998. In this paper we analyze bounds ... See full document

... study of the distance closed dominating sets in graphs are studied in [6].In this paper,the distance closed domatic number of some special classes of graphs are studied.Also, a general ... See full document

... The Fuzzy Directed Graph, Fuzzy competition digraphs are well known topic.The concept of domination in fuzzy graphs are introduced by A. Somasundaram and S. Somasundaram [] in 1998. In this paper we analyze bounds ... See full document

... –partition. Dominating complementary color transversal set of G is a dominating set which is also transversal of a χ - partition of the graph, such a set with minimum cardinality is called ... See full document

... Edge-Vertex Dominating Sets of Cycles Let Dev Cn , i be the family of ev-dominating sets of Cn with cardinality i.. We investigate the ev-dominating sets of Cn.[r] ... See full document

... a dominating set of G, if NS V , or equivalently, every vertex in V \S is adjacent to at least one vertex in ...the minimum cardinality of a dominating set in G. A dominating set with ... See full document

... prime dominating set is obtained by choosing m vertices from A and a vertex from B. The m vertices from A can be cho- sen in one way and a vertex from B can be selected in n ways. Therefore, the number of ways of ... See full document

... f (u) ≥ 1 for every vertex v ∈ V (G) and for at least one vertex of w ∈ V (G), f (N[w]) = +1. The weight of f , denoted by w( f ) is the sum of the values f (v) for all v ∈ V (G). An isolated signed domination number of ... See full document

... minimal dominating sets of ...entire dominating transformation graph G xyz is the graph having V∪S as the vertex set and for any two vertices u and v in V∪S, u and v are adjacent if and only if one ... See full document

... convex dominating set of 𝐺 with |𝑆| ≥ 3 , 𝐶 = ⋃ 𝑥∈𝑆 ({𝑥} × 𝑇 𝑥 ) is a weakly convex dominating set of 𝐺[𝐻] by Remark ...connected dominating set of ... See full document