Let G = (V,E) be a graph. A subset S ⊆ V is a dominating set of G if every vertex not in S is adjacent to a vertex in S. A set D̃ ⊆ V of a graph G = (V,E) is called an outer-connected dominating set for G if (1) D̃ is a dominating set for G, and (2) G[V \ D̃], the induced subgraph of G by V \ D̃, is connected. The minimum size among all outer-connected dominating sets of G is called the outerconnec...

An edge dominating set of a graph is said to be an odd (even) sum degree (osded (esded) - set) G if the all edges in X number. The domination number minimum cardinality taken over sets and defined as zero no such exists G. In this paper, concept extended on co-dominating E-T G, where T corresponding parameters co-odd set, value defined. Further, exact values above are found for some standard cl...

This paper is devoted to the online dominating set problem and its variants on trees, bipartite, bounded-degree, planar, and general graphs, distinguishing between connected and not necessarily connected graphs. We believe this paper represents the first systematic study of the effect of two limitations of online algorithms: making irrevocable decisions while not knowing the future, and being i...

In this paper we study cooperative cost games arising from domination problems on graphs. We introduce three games to model the cost allocation problem and we derive a necessary and sufficient condition for the balancedness of all three games. Furthermore we study concavity of these games.

We study the approximability of the weighted edge-dominating set problem. Although even the unweighted case is NP-Complete, in this case a solution of size at most twice the minimum can be efficiently computed due to its close relationship with minimum maximal matching; however, in the weighted case such a nice relationship is not known to exist. In this paper, after showing that weighted edge ...

Let G be a graph with vertex set V (G). A function f : V (G) → {−1, 1} is a signed dominating function of G if, for each vertex of G, the sum of the values of its neighbors and itself is positive. The signed domination number of a graph G, denoted γs(G), is the minimum value of ∑ v∈V (G) f(v) over all the signed dominating functions f of G. The signed reinforcement number of G, denoted Rs(G), i...

Efficient routing among mobile hosts is an important function in ad hoc networks. Routing based on a connected dominating set is a promising approach, where the search space for a route is reduced to the hosts in the set. A set is dominating if all the hosts are either in the set or neighbors of hosts in the set. The efficiency of dominating-set-based routing mainly depends on the overhead intr...

Given a graph, a connected dominating set is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected.A minimum connected dominating set is such a vertex subset with minimum cardinality. In this paper, we present a new one-step greedy approximation with performance ratio ln + 2 where is the maxi...

We study distributed algorithms for three graph-theoretic problems in weighted trees and weighted planar graphs. For trees, we present an efficient deterministic distributed algorithm which finds an almost exact approximation of a maximum-weight matching. In addition, in the case of trees, we show how to approximately solve the minimum-weight dominating set problem. For planar graphs, we presen...

An independent dominating set D of a graph G = (V,E) is a subset of vertices such that every vertex in V \ D has at least one neighbor in D and D is an independent set, i.e. no two vertices of D are adjacent in G. Finding a minimum independent dominating set in a graph is an NP-hard problem. Whereas it is hard to cope with this problem using parameterized and approximation algorithms, there is ...