[PDF] Top 20 MORE RESULTS ON COMPLEMENTARY TREE NIL DOMINATION NUMBER OF A GRAPH

... a graph G, let V(G) and E(G) denote its vertex set and edge set ...resulting graph is the subdivision graph S(G). The concept of domination in graphs was introduced by ...a graph G is a ... See full document

... minimal dominating set of G is called domination number of G which is denoted by . The open neighborhood N( of V(G) is the set of vertices adjacent to and the set N[ =N ∪ is the closed neighborhood of For ... See full document

... a complementary tree dominating set of ...a graph obtained from a path by attaching pendent vertices to atleast one of its end ...Type results: ... See full document

... a domination parameter and a graph theoretic parameter and characterized the corresponding extremal ...similar results for and ...the complementary perfect domination number and ... See full document

... Let us observe that all classes mention above are hereditary, i.e. closed under taking induced subgraphs. It is well-known (and not difficult to see) that a class of graphs is hereditary if and only if it can be ... See full document

... : Domination Theory is an important branch of Graph Theory that has wide range of applications to various branches of Science and ...triple domination number of G and is denoted by  x 3 (G) ... See full document

... of graph theoretic parameters have been used to derive formulas to calculate network ...The graph vulnerability relates to the study of graph when some of its elements (vertices or edges) are ...of ... See full document

... the domination in graphs has been an evergreen of the graph ...the domination number. The theory of domination in graphs was introduced by ...on results and applications of ... See full document

... In this paper, upper bound of the sum of total domination and chromatic number is proved. In future this result can be extended to various domination parameters. The structure of the graphs had been ... See full document

... In 1962, ore used the name “dominating set” and “domination number” for the same concept. In 1977, Cockayne and Hedetniemi made an interesting and extensive survey of the results known at that time ... See full document

... sub graph of G induced by ...of graph G , denoted by N(S) is the set of all vertices adjacent to some vertex in S, and N ( S ) ∪ S is called the closed neighbourhood of S, denoted by ...connected ... See full document

... a graph G = (V, E) is a dominating set, if every vertex in V(G) - D is adjacent to some vertex in ...The domination number γ(G) of G is the minimum cardinality of a dominating ...two ... See full document

... A recent application of the convex hull is the Onion Technique for linear optimization queries. This method is based on a theorem that a point which maximizes an arbitrary multidimensional weightening function can be ... See full document

... a graph G = (V, E) is a dominating set, if every vertex in V(G) – D is adjacent to some vertex in ...The domination number γ (G) of G is the minimum cardinality of a dominating ...a ... See full document

... edge domination number, ( )of is the minimum cardinality of an edge dominating sets of , , , , , ...edge domination number ( )of is the minimum cardinality taken over all total edge dominating ... See full document

... Let G = (V, E) be any connected graph with at least two vertices. Adouble geodetic dominating set of G is a subset S of V(G) which is both dominating and double geodetic set of G. A double geodetic dominating set ... See full document

... In the past some years intensely those Graphsstudied whose drawings can be viewed as approximations to the famous Sierprińskitriangle. The curiosity for thesegraphs comes from many diverse sources such as games like the ... See full document

... the domination number of G is (G) = that means the domination number of the graph G is equal to the number of sets each contains 2k+1 ...the domination number of G ... See full document

... Proof: Since every vertex in V-D is adjacent to exactly one vertex in D. It implies that every two vertices in V-D and adjacent. As J(G) is n-regular every vertex in D is adjacent to some vertex in V-D. Suppose that ... See full document

... Proof. In 𝐹(𝑘 𝑛 ) all the edges are strong. Let x = (u, v) be any edge in 𝐹(𝑘 𝑛 ). Since 𝐹(𝑘 𝑛 ) is complete there are n-2 edges incident at u and v other than the edge x. Therefore the edge x dominates 2n-4 edges. The ... See full document