Let G = (V, E) be a graph with chromatic number χ(G). A dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every χ-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by γct(G). In this paper we characterize the class of trees, unicyclic graphs and c...

For a graph G a subset D of the vertex set of G is a k-dominating set if every vertex not in D has at least k neighbors in D. The k-domination number γk(G) is the minimum cardinality among the k-dominating sets of G. Note that the 1-domination number γ1(G) is the usual domination number γ(G). Fink and Jacobson showed in 1985 that the inequality γk(G) ≥ γ(G) + k − 2 is valid for every connected ...

The domination number of graph is the smallest cardinality set G. A subset a vertex S G called if every element dominates G, meaning that not an connected and one distance from S. has become interesting research studies on several graphs k -connected such as circulant graphs, grids, wheels. This study aims to determine other k-connected Harary graph. method used pattern detection axiomatic dedu...

for every positive integer k, a set s of vertices in a graph g = (v;e) is a k- tuple dominating set of g if every vertex of v -s is adjacent to at least k vertices and every vertex of s is adjacent to at least k - 1 vertices in s. the minimum cardinality of a k-tuple dominating set of g is the k-tuple domination number of g. when k = 1, a k-tuple domination number is the well-studied domination...

A paired-dominating set of a graph is a dominating set of vertices whose induced subgraph has a perfect matching, while the paired-domination number is the minimum cardinality of a paired-dominating set in the graph. Recently, Chen, Sun and Xing [Acta Mathematica Scientia Series A Chinese Edition 27(1) (2007), 166–170] proved that a cubic graph has paired-domination number at most three-fifths ...