[PDF] Top 20 Secure Complementary Tree Domination Number of a Graph

... Let D be minimal. Assume the contrary, if there exists a vertex v of D such that v does not satisfy any of the given conditions, then by (i) and (ii), the set = D – {v} is a dominating set. By (iii) < V – > is ... See full document

... a graph G is called a component of G .The number of components of G is denoted by ...the graph with vertex set V in which two vertices are adjacent iff they are not adjacent in ...A tree is a ... See full document

... induced complementary perfect domination number of G and denoted by X icp (G ) ...induced complementary perfect domination set of a graph G (icpd-set) is a domination set ... See full document

... a domination parameter and a graph theoretic parameter and characterized the corresponding extremal ...the complementary perfect domination number and proved that (G)+ ≤ 2n-2, and ... See full document

... Proof: Let G be a connected graph. Then every two vertices in G are connected. Let u ∈ R be the vertex of degree p ‒ 1. Then N [u] = V(G). Thus we have the Semi – Complementary Splitting graph G such ... See full document

... Proof. Let be any non-trivial tree with ≥ 3. It can be verified that the result istrue for = 3. Since if = 3 then = . Now consider the case that > 3. Since has atleast one vertex with degree greater than or ... 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

... of complementary tree nil dominating set is introduced in ...a complementary tree nil dominating set (ctnd-set) if the induced subgraph < V(G) D > is a tree and the set V(G) - D ... 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

... of domination in graphs was introduced by Ore ...The domination number γ( G) of G is the minimum cardinality of a dominating ...Many domination parameters are obtained by combining ... See full document

... 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

... a graph G, let V(G) and E(G) denote its vertex set and edge set ...A graph with p vertices and q edges is denoted by G(p, ...of domination in graphs was introduced by ...the domination ... See full document

... number h(G) of G is the minimum order of its hull sets and any hull set of order h(G) is a minimum hull set or simply a h- set of G. A vertex x is said to lie on a u-v monophonic path P if x is a vertex of P ... See full document

... The network topology is significant since the communication between processors is de- rived via message exchange in distributed systems. For this reason, a communication network is modeled by a graph to measure ... See full document

... connected graph of order . The total edge dominating set in a connected graph is called a minimal total edge dominating set if no proper subset of is a total edge dominating set of ...edge domination ... 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

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

... Circular-arc graphs are introduced as generalization of interval graphs. The class of interval graphs is properly contained in the class of circular-arc graphs. In fact every interval graph is a Circular-arc ... See full document

... p-reinforcement number of graphs is found in ...p-reinforcement number of some graphs such as paths, cycles and complete t-partite graphs, and established some upper ...2-reinforcement number equal ... See full document

... Now let g : E(G) → {1, 2}) . By the definition of line graph, there exist a 1-1 and on-to function between the vertices of line graph of G, i.e., V(H), and edges of G , i.e., E(G) ,such that g (e i ) = g(v ... See full document