[PDF] Top 20 ON THE AVERAGE LOWER 2-DOMINATION NUMBER OF A GRAPH

... 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

... wheel graph has been used in different areas such as the wireless sensor networks, the vulnerability of networks, and so ...wheel graph has many good ...neighborhood graph of the hub ...friendship ... See full document

... The average distance can be used as a tool in analytic networks where the performance time is proportions to the distance between any two ...the average case as opposed to the diameter, which indicates the ... See full document

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

... a graph G = ( V, E ) is called an independent majority dominating (IMD) set if the induced sub graph < D > has no ...called lower majority independent set of G and it is also called the ... See full document

... of domination for Cayley graphs has been studied by various authors ...efficient domination number for vertex transitive graphs has been obtained by Jia Huang and Jun-Ming Xu ...perfect ... See full document

... Graph theory is already utilized on flight networks. Airlines want to connect countless cities in the most efficient way, moving the most passengers with the fewest possible trips a problem very similar to the ... See full document

... a graph we mean a finite, simple, connected and undirected graph G = (V,E), where V is the vertex set and E is the edge set of ...the graph G has p vertices and q ...[1, 2, 13, ... See full document

... complete graph K k and S (n , 3 ) are the graphsof problem of Hanoi ...Section 2], found the isomorphism betweenHanoi graphs and a sequence of graphs obtained from approximations to theSierprińskitriangle ... See full document

... connected graph, then a set S of vertices is a geodetic set if I[S] = ...geodetic number of G, and is denoted by g(G). The geodetic number of a disconnected graph is the sum of the geodetic ... See full document

... connected graph of order ...geodetic domination number of and is denoted by ( ...connected graph is called a minimal open geodetic dominating set of if no proper subset of is an open geodetic ... 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

... a graph G = (V,E), we mean a finite undirected connected graph without loops or multiple ...finite graph convexity space is a pair (V, E), formed by a finite connected graph G = (V, E) and a ... See full document

... Proof: By Recursive Construction 1, there are 2 copies of BF(3k) and a level with 2 3k+1 vertices in BF(3k+1). Let D denote a triple dominating set of BF(3k+1). Consider the vertices in a minimum triple ... 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 ...≤ 2 for some ... See full document

... 2) Proof: Roman Emperor Constantine had the requirement that an army or legion could be sent from its home to defend a neighboring location only if there was a second army, which would stay and protect the home. ... See full document

... of Domination in Graphs, Marcel ...split domination number of ...split domination number of a graph, Graph theory Notes of New York Academy of Sciences XXXII pp ... 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 ...acyclic ... See full document

... p-reinforcement number of G, denoted by r p (G ) , is the minimum number of edges in G C that has to be added to G in order to reduce the p-domination number of the resulting ... See full document