The complete cototal domination set is said to be irredundant dominating if for each u ∈ S, NG [S − {u}] ≠ [S]. minimum cardinality taken over all an called number and denoted by γircc(G). Here a new parameter was introduced the study of bounds γircc(G) initiated.

A set $S subseteq V(G)$ is a semitotal dominating set of a graph $G$ if it is a dominating set of $G$ andevery vertex in $S$ is within distance 2 of another vertex of $S$. Thesemitotal domination number $gamma_{t2}(G)$ is the minimumcardinality of a semitotal dominating set of $G$.We show that the semitotal domination problem isAPX-complete for bounded-degree graphs, and the semitotal dominatio...

Wireless ad hoc networks are advancing rapidly, both in research and more and more into our everyday lives. Wireless sensor networks are a prime example of a new technology that has gained a lot of attention in the literature, and that is going to enhance the way we view and interact with the environment. These ad hoc and sensor networks are modeled by communication graphs which give the commun...

A 2-rainbow dominating function ( ) of a graph  is a function  from the vertex set  to the set of all subsets of the set  such that for any vertex  with  the condition  is fulfilled, where  is the open neighborhood of . A maximal 2-rainbow dominating function on a graph  is a 2-rainbow dominating function  such that the set is not a dominating set of . The weight of a maximal    is the value . ...

Service discovery is a crucial feature for the usability of mobile ad-hoc networks (MANETs). In this paper, Minimum Dominating Forward Node Set based Service Discovery Protocol (MDFNSSDP) is proposed. MDFNSSDP has the following characteristics: 1)It minimizes the number of coverage demanding nodes in the current node’s 2-hop neighbor set. 2) It minimizes the size of dominating forward node set ...

A Connected Dominating Set (CDS) of the graph representing a Wireless Sensor Network can be used as a virtual backbone for routing in the network. Since sensor nodes are constrained by limited on-board batteries, it is desirable to have a small CDS for the network. However, constructing a minimum size CDS has been shown to be a NP-hard problem. In this paper we present a distributed greedy algo...

This paper addresses the problem of scatternet formation and maintenance for multi-hop Bluetooth based personal area and ad hoc networks with minimal communication overhead. Each node is assumed to know its position and position of all its neighbours. The proposed formation algorithms have three phases. In the first phase the unit graph is constructed (each node establishes connection with all ...

A set S ⊆ V (G) is a restrained strong resolving hop dominating in G if for every v ∈ (G)\S, there exists w such that dG(v, w) = 2 and or (G)\S has no isolated vertex. The smallest cardinality of set, denoted by γrsRh(G), called the domination number G. In this paper, we obtained corresponding parameter graphs resulting from join, corona lexicographic product two graphs. Specifically, character...

Multipoint relays o er an optimized way of ooding packets in a radio network. However, this technique requires the last hop knowledge: to decide wether or not a ooding packet is retransmitted, a node needs to know from which node the packet was received. When considering broadcasting at IP level, this information may be di cult to obtain. We thus propose a scheme for computing an optimized conn...