Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of… Expand

It is shown that the power dominating set (PDS) problem is NP-complete even when restricted to bipartite graphs or chordal graphs and a linear algorithm is given to solve the PDS for trees.Expand

The domatic number of a graph is defined and studied and it is seen that the theory of domination resembles the well known theory of colorings of graphs.Expand

LP-duality, complementarity and generality of graphical subset parameters dominating functions in graphs fractional domination and related parameters majority domination and its generalizations… Expand

Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network that one individual has an item of information which needs to be communicated to everyone else.Expand

An algorithm is presented which determines the amount of time required to pass, or to broadcast, a unit of information from an arbitrary vertex to every other vertex in a tree and it is shown that the subtree induced by the broadcast center of a tree is always a star with two or more vertices.Expand

Results concerning the total domination number of G (the smallest number of vertices in a total dominating set) and the total domatic number ofG (the largest order of a partition of G into total dominating sets) are obtained.Expand

While there is a polynomial-time algorithm to determine whether χb(G) ≤ 3, it is shown that it is NP-hard to determine if π(u) ≤ 4, and the maximum broadcast chromatic number of a tree is determined.Expand