[PDF] Top 20 Dominating and Total Dominating Complementary Color Transversal number of Graphs

... (Chromatic number) The chromatic number of a graph G is the smallest value of n such that G admits a proper n – ...This number is denoted as χ ... See full document

... minimal dominating sets of ...minimal dominating set of G. x = – if u, v ∉ D where D is a minimal dominating set of ...entire dominating transformation graphs in domination ... See full document

... dominating--color number of G. Instead of dominating set in the definition of dominating--color number, if we consider strong dominating set, then it is called ... See full document

... a dominating set is called the domination number of G and is denoted by γ ...in graphs in [9]. A set D ⊆ V is called a weak dominating set if for every vertex v ∈ V − D, there exists a vertex ... See full document

... sub graphs of and are isomorphic to cycle and copies of that has dominating color number is either 2 or ...same color. So, adding the edges to connect the induced sub-graphs and ... 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 and ... See full document

... A dominating set for a graph G is a subset D of V such that every vertex not in D is adjacent to at least one member of ...the graphs having unique minimum dominating ...minimum dominating ... See full document

... in graphs. A dominating set S of a graph G is said to be an isolate dominating set, if < S > has at least one isolated vertex ...isolate dominating set S is said to be minimal if no ... See full document

... prime dominating set of a graph ...prime dominating set if it is a dominating set with at least two elements and for every pair of vertices u and v in S such that (deg u, deg v) = ...prime ... See full document

... prime dominating set if it is a dominating set and for every pair of vertices u and v in S such that (d(u), d(v)) = ...prime dominating set is called the relatively prime domination number and ... See full document

... of graphs. Graphs associated with certain arithmetic functions which are usually called arithmetic graphs have been studied extensively by many ...minimal total dominating functions and ... See full document

... etc. Number Theory is one of the oldest branches of Mathematics, which inherited rich contributions from almost all greatest mathematicians, ancient and ...the number theoretic function Euler totient ... See full document

... Similar to energies like Laplacian energy, distance energy, minimum covering energy, incidence energy [3,4, 5, 6, 7], the double dominating energy is defined in this paper and same is [r] ... See full document

... fuzzy graphs such as semi complementary fuzzy graph and semi complete fuzzy graph are ...Semi complementary and Semi complete fuzzy graphs are ...its number of fuzzy graphs are ... 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

... a total dominating set with cardinality ௡ିଷ ଶ + 2 = ௡ାଵ ଶ ...a Transversal of ૏ − partition of G formed by such ૏ − Coloring of G and this set S is a minimum total dominating ... See full document

... equitable dominating set of is called the equitable domination number of and is denoted by ( ...power dominating set (PDS) 6 of if every vertex ∈ − is observed by some vertices in using the following ... See full document

... (ii) If an observed vertex in has > 1 adjacent vertices and if − 1 of these vertices are already observed, then the remaining one non-observed vertex is also observed by in . The minimum cardinality of a power ... 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

... of graphs. An introduction and an extensive overview on domination in graphs and related topics is surveyed and detailed in the two books by Haynes et al [7, ...in graphs while the fractional edge ... See full document