For a graph G = (V,E), a subset D ⊆ V (G) is a total dominating set if every vertex of G has a neighbor in D. The total domination number of G is the minimum cardinality of a total dominating set of G. A subset D ⊆ V (G) is a 2-dominating set of G if every vertex of V (G) \ D has at least two neighbors in D, while it is a 2-outer-independent dominating set of G if additionally the set V (G) \ D...

A quasi-hamiltonian path in a semicomplete multipartite digraph D is a path which visits each maximal independent set (also called a partite set) of D at least once. This is a generalization of a hamiltonian path in a tournament. In this paper we investigate the complexity of finding a quasi-hamiltonian path, in a given semicomplete multipartite digraph, from a prescribed vertex x to a prescrib...

In [8] an algorithm has been presented that computes a maximal independent set (MIS) withinO(log n/F + log n polyloglogn) rounds in an n-node multichannel radio network with F commu-nication channels. The paper uses a multichannel variant of the standard graph-based radio networkmodel without collision detection and it assumes that the network graph is a polynomially bounded in-...

People arrive one at a time to a theater consisting of m rows of length n. Being unfriendly they choose seats at random so that no one is in front of them, behind them or to either side. What is the expected number of people in the theater when it becomes full, i.e., it cannot accommodate any more unfriendly people? This is equivalent to the random process of generating a maximal independent se...

Generating all configurations that satisfy a given specification is a well-studied problem in Combinatorics and in Graph theory suggesting many interesting problems. Among them, generating all maximal independent sets of a given graph is one that has attracted considerable attention [3,4,7]. A maximal independent set of a graph G = (V,E) is a subset V ′ ⊆ V such that no two vertices in V ′ are ...

Virtual backbone has been used extensively in various aspects for wireless ad hoc or sensor networks recently. We propose an approximation solution to construct a virtual backbone based on a more generalized and realistic model of polynomial bounded growth. A localized distributed algorithm of MCDS_GBG for computing a Minimum Connected Dominating Sets as backbone in the growth-bounded graph is ...

A subset S ⊆ V (G) is an independent set of G if no two vertices of S are adjacent in G. A subset Q ⊆ V (G) is a 2-dominating set of G if each vertex from V (G)\Q has at least two neighbours in Q. We define new kind of kernels in graphs. Using existing concepts of an independent set and a 2-dominating set, we define in the natural way the concept of 2-dominating kernels in graphs. A subset J ⊂ ...

A subset S of V is called a total dominating set if every vertex in V is adjacent to some vertex in S. The total domination number γt (G) of G is the minimum cardinality taken over all total dominating sets of G. A dominating set is called a connected dominating set if the induced subgraph 〈S〉 is connected. The connected domination number γc(G) of G is the minimum cardinality taken over all min...

A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input graph G without cycles of length 4, 5, and 6, we cha...

We prove that every (claw, net)-free graph contains an induced doubly dominating cycle or a dominating pair. Moreover, using LexBFS we present a linear time algorithm which, for a given (claw, net)-free graph, 3nds either a dominating pair or an induced doubly dominating cycle. We show also how one can use structural properties of (claw, net)-free graphs to solve e4ciently the domination, indep...