[PDF] Top 20 Strong Dominating Sets of Some Arithmetic Graphs

... of graphs, namely “Arithmetic ...various Arithmetic graphs in which adjacency between vertices is defined through various arithmetic ... See full document

... in graphs is a flourishing area of research at present. Dominating sets play an important role in practical applications, such as logistics and networks design, mobile computing, resource allocation ... See full document

... We now show that is minimal. Suppose we delete a vertex, say from Obviously this vertex is not dominated by any vertex in as are primes, there is no adjacency between these vertices in Therefore can’t be a ... See full document

... Fuzzy graphs were introduced by Rosenfeld ...established some of their properties ...of strong arcs [7]. Different parameters like sum distance in fuzzy graphs and chromatic number of fuzzy ... See full document

... efficient dominating sets, all efficient dominating sets have the same cardinality namely 𝛾 ...of strong efficient domination. The maximum cardinality of any strong efficient ... See full document

... in graphs has been an extensively research branch of graph ...3]). Dominating sets play an important role in practical applications, such as allocation of re-hydrants or serving sites of other ... See full document

... a dominating set of G if every vertex in V − S is adjacent to at least one vertex in ...all dominating sets in ...A dominating set is said to be restrained dominating set if every ... See full document

... define strong dominating  - color number of a graph G as the maximum number of color classes which are strong dominating sets of G, and is denoted by sd  (G) , where the maximum is ... See full document

... a dominating set is called the domination number of G and is denoted by γ ...of strong (weak) domination in graphs in ...weak dominating set if for every vertex v ∈ V − D, there exists a ... See full document

... Then the direct product of these two graphs denoted by is defined to be a graph with vertex set , where is the Cartesian product of the sets and such that any two distinct vertices and o[r] ... See full document

... minimal dominating set of G containing ...minimal dominating graph CD(G) of G in the graph having the same vertex set as G with two vertices in CD(G) adjacent if u, v ∈ D where D is a minimal ... 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 dominating ... 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

... Apart from the above given basic definitions, there exists a few more concepts related to connectivity which play an important role in applications of weighted graphs. Next we present a few of them, which includes ... See full document

... need to consider P i−1 n−1 , P i−1 n−2 , and P i−1 n−3 . The families of these dominating sets can be empty or otherwise. Thus, we have eight combinations of whether these three families are empty or not. ... See full document

... By a graph G = (V,E ) we mean a finite undirected graph without loops and multiple edges. The order and size of G are denoted by n and m respectively. For graph theoretical terms, we refer to Harary [5] and for terms ... See full document

... e uv  say " u and v are adjacent". Chemical graph theory is an important branch of graph theory and Mathematical chemistry, which applies graph theory to mathematical modeling of chemical phenomena [7, 9, 10, ... See full document

... finite arithmetic progression of positive integers with the ini- tial value a and the constant difference ...are arithmetic progres- sions that have no representation as an ... See full document

... By using the definition of signed dominating function and isolate domination, we introduced the concept of isolated signed dominating function. An isolated signed dominat- ing function (ISDF) of a graph G ... See full document

... independent dominating set (Haynes et ...a dominating set of a graph is a strong split dominating set if the induced subgraph is totally disconnected with at least two ...The strong ... See full document