In this paper, a new multi-hop weighted clustering procedure is proposed for homogeneous Mobile A... more In this paper, a new multi-hop weighted clustering procedure is proposed for homogeneous Mobile Ad hoc networks. The algorithm generates double star embedded non-overlapping cluster structures, where each cluster is managed by a leader node and a substitute for the leader node (in case of failure of leader node). The weight of a node is a linear combination of six different graph theoretic parameters which deal with the communication capability of a node both in terms of quality and quantity, the relative closeness relationship between network nodes and the maximum and average distance traversed by a node for effective communication. This paper deals with the design and analysis of the algorithm and some of the graph theoretic/structural properties of the clusters obtained are also discussed.
In this paper, a new parameter on domination is defined by imposing a restriction on the degrees ... more In this paper, a new parameter on domination is defined by imposing a restriction on the degrees of vertices in the dominating set. For a positive integer k, a dominating set D of a graph G is said to be a k-part degree restricted dominating set (k-DRD-set), if for all u ∈ D there exists a set Cu ⊆ N(u) ∩ (V − D) such that \(|C_u| \leq \lceil \frac {d(u)}{k}\rceil \) and ⋃u ∈ DCu = V − D. The minimum cardinality of a k-part degree restricted dominating set of G is called the k-part degree restricted domination number of G and is denoted by \(\gamma _{\frac {d}{k}}(G)\). Here, we determine the k-part degree restricted domination number of some well-known graphs, relation between dominating and k-DRD set, and an algorithm which verifies whether a given dominating set is a k-DRD set or not.
For a positive integer k, a dominating set D of a graph G is said to be a k-part degree restricte... more For a positive integer k, a dominating set D of a graph G is said to be a k-part degree restricted dominating set (k-DRD set) if for all u ∈ D, there exists a set Cu ⊆ N(u)∩(V−D) such that |Cu| ≤ ⌈ d(u) k ⌉ and ∪u∈DCu = V −D. The minimum cardinality of a k-DRD set of a graph G is called the k-part degree restricted domination number of G and is denoted by γ d k (G). In this paper, we provide some bounds on γ d k of join of two graphs, bounds on γ d k in terms of maximum degree, independence number and covering number. Further, we discuss some Nordhaus-Gaddum type results. In addition to this, we prove that for any graph G, γ d k (G) ≤ γk(G), where γk(G) is the k-domination number of G and we characterize the trees T for which γ d k (T ) = γk(T ).
This paper deals with the design and analysis of the distributed weighted clustering algorithm SD... more This paper deals with the design and analysis of the distributed weighted clustering algorithm SD_DWCA proposed for homogeneous mobile ad hoc networks. It is a connectivity, mobility and energy based clustering algorithm which is suitable for scalable ad hoc networks. The algorithm uses a new graph parameter called strong degree defined based on the quality of neighbours of a node. The parameters are so chosen to ensure high connectivity, cluster stability and energy efficient communication among nodes of high dynamic nature. This paper also includes the experimental results of the algorithm implemented using the network simulator NS2. The experimental results show that the algorithm is suitable for high speed networks and generate stable clusters with less maintenance overhead.
A dominating set $S $ of a graph $ G $ is an \textit{efficient dominating set} (EDS) of $G$ if $|... more A dominating set $S $ of a graph $ G $ is an \textit{efficient dominating set} (EDS) of $G$ if $|N_G[v]\cap S|=1$, for all $v\in V(G)$. $G$ is \textit{efficiently dominatable} or \textit{efficient} if it has an EDS. Not all graphs are efficient. The class of efficient graphs is denoted by $\mathscr{E}$. If $G\in \mathscr{E}$, then any EDS of $G$ has its cardinality equal to the domination number of $G$, denoted by $\gamma(G)$. An edge $e\in E(\overline{G})$ is \textit{critical} or $\gamma$-\textit{critical} if $\gamma(G+e)\ne \gamma(G)$. The study of critical concepts exists for domination and its variants. We extend this study to graphs which are efficient. This paper deals with the study of the properties of critical edges of graphs in $ \mathscr{E} $. Depending on whether the addition of an edge increases or decreases or leaves unaltered $\gamma(G)$, the edge set of $ G $ is classified respectively into three sets: $EA^+$, $EA^-$, $EA^0$. To study the changing and unchanging prop...
The concept of network is predominantly used in several applications of computer communication ne... more The concept of network is predominantly used in several applications of computer communication networks. It is also a fact that the dominating set acts as a virtual backbone in a communication network. These networks are vulnerable to breakdown due to various causes, including traffic congestion. In such an environment, it is necessary to regulate the traffic so that these vulnerabilities could be reasonably controlled. Motivated by this, [Formula: see text]-part degree restricted domination is defined as follows. For a positive integer [Formula: see text], a dominating set [Formula: see text] of a graph [Formula: see text] is said to be a [Formula: see text]-part degree restricted dominating set ([Formula: see text]-DRD set) if for all [Formula: see text], there exists a set [Formula: see text] such that [Formula: see text] and [Formula: see text]. The minimum cardinality of a [Formula: see text]-DRD set of a graph [Formula: see text] is called the [Formula: see text]-part degree r...
International Journal of Wireless & Mobile Networks (IJWMN), 2011
In this paper, a new multi-hop weighted clustering procedure is proposed for homogeneous Mobile A... more In this paper, a new multi-hop weighted clustering procedure is proposed for homogeneous Mobile Ad hoc networks. The algorithm generates double star embedded non-overlapping cluster structures, where each cluster is managed by a leader node and a substitute for the leader node (in case of failure of leader node). The weight of a node is a linear combination of six different graph theoretic parameters which deal with the communication capability of a node both in terms of quality and quantity, the relative closeness relationship between network nodes and the maximum and average distance traversed by a node for effective communication. This paper deals with the design and analysis of the algorithm and some of the graph theoretic/structural properties of the clusters obtained are also discussed.
In this paper, we propose a new distributed weighted clustering algorithm for MANETs by introduci... more In this paper, we propose a new distributed weighted clustering algorithm for MANETs by introducing a new graph parameter called strong degree defined based on the quality of neighbors of a node. The proposed algorithm is a cluster-head based algorithm. The ...
In this paper, we propose a new multi-parameter weight based double star embedded clustering algo... more In this paper, we propose a new multi-parameter weight based double star embedded clustering algorithm for MANETs. The weight of a node is a linear combination of six different graph theoretic parameters which deal with the communication capability of a node both ...
In this paper, a new multi-hop weighted clustering procedure is proposed for homogeneous Mobile A... more In this paper, a new multi-hop weighted clustering procedure is proposed for homogeneous Mobile Ad hoc networks. The algorithm generates double star embedded non-overlapping cluster structures, where each cluster is managed by a leader node and a substitute for the leader node (in case of failure of leader node). The weight of a node is a linear combination of six different graph theoretic parameters which deal with the communication capability of a node both in terms of quality and quantity, the relative closeness relationship between network nodes and the maximum and average distance traversed by a node for effective communication. This paper deals with the design and analysis of the algorithm and some of the graph theoretic/structural properties of the clusters obtained are also discussed.
In this paper, a new parameter on domination is defined by imposing a restriction on the degrees ... more In this paper, a new parameter on domination is defined by imposing a restriction on the degrees of vertices in the dominating set. For a positive integer k, a dominating set D of a graph G is said to be a k-part degree restricted dominating set (k-DRD-set), if for all u ∈ D there exists a set Cu ⊆ N(u) ∩ (V − D) such that \(|C_u| \leq \lceil \frac {d(u)}{k}\rceil \) and ⋃u ∈ DCu = V − D. The minimum cardinality of a k-part degree restricted dominating set of G is called the k-part degree restricted domination number of G and is denoted by \(\gamma _{\frac {d}{k}}(G)\). Here, we determine the k-part degree restricted domination number of some well-known graphs, relation between dominating and k-DRD set, and an algorithm which verifies whether a given dominating set is a k-DRD set or not.
For a positive integer k, a dominating set D of a graph G is said to be a k-part degree restricte... more For a positive integer k, a dominating set D of a graph G is said to be a k-part degree restricted dominating set (k-DRD set) if for all u ∈ D, there exists a set Cu ⊆ N(u)∩(V−D) such that |Cu| ≤ ⌈ d(u) k ⌉ and ∪u∈DCu = V −D. The minimum cardinality of a k-DRD set of a graph G is called the k-part degree restricted domination number of G and is denoted by γ d k (G). In this paper, we provide some bounds on γ d k of join of two graphs, bounds on γ d k in terms of maximum degree, independence number and covering number. Further, we discuss some Nordhaus-Gaddum type results. In addition to this, we prove that for any graph G, γ d k (G) ≤ γk(G), where γk(G) is the k-domination number of G and we characterize the trees T for which γ d k (T ) = γk(T ).
This paper deals with the design and analysis of the distributed weighted clustering algorithm SD... more This paper deals with the design and analysis of the distributed weighted clustering algorithm SD_DWCA proposed for homogeneous mobile ad hoc networks. It is a connectivity, mobility and energy based clustering algorithm which is suitable for scalable ad hoc networks. The algorithm uses a new graph parameter called strong degree defined based on the quality of neighbours of a node. The parameters are so chosen to ensure high connectivity, cluster stability and energy efficient communication among nodes of high dynamic nature. This paper also includes the experimental results of the algorithm implemented using the network simulator NS2. The experimental results show that the algorithm is suitable for high speed networks and generate stable clusters with less maintenance overhead.
A dominating set $S $ of a graph $ G $ is an \textit{efficient dominating set} (EDS) of $G$ if $|... more A dominating set $S $ of a graph $ G $ is an \textit{efficient dominating set} (EDS) of $G$ if $|N_G[v]\cap S|=1$, for all $v\in V(G)$. $G$ is \textit{efficiently dominatable} or \textit{efficient} if it has an EDS. Not all graphs are efficient. The class of efficient graphs is denoted by $\mathscr{E}$. If $G\in \mathscr{E}$, then any EDS of $G$ has its cardinality equal to the domination number of $G$, denoted by $\gamma(G)$. An edge $e\in E(\overline{G})$ is \textit{critical} or $\gamma$-\textit{critical} if $\gamma(G+e)\ne \gamma(G)$. The study of critical concepts exists for domination and its variants. We extend this study to graphs which are efficient. This paper deals with the study of the properties of critical edges of graphs in $ \mathscr{E} $. Depending on whether the addition of an edge increases or decreases or leaves unaltered $\gamma(G)$, the edge set of $ G $ is classified respectively into three sets: $EA^+$, $EA^-$, $EA^0$. To study the changing and unchanging prop...
The concept of network is predominantly used in several applications of computer communication ne... more The concept of network is predominantly used in several applications of computer communication networks. It is also a fact that the dominating set acts as a virtual backbone in a communication network. These networks are vulnerable to breakdown due to various causes, including traffic congestion. In such an environment, it is necessary to regulate the traffic so that these vulnerabilities could be reasonably controlled. Motivated by this, [Formula: see text]-part degree restricted domination is defined as follows. For a positive integer [Formula: see text], a dominating set [Formula: see text] of a graph [Formula: see text] is said to be a [Formula: see text]-part degree restricted dominating set ([Formula: see text]-DRD set) if for all [Formula: see text], there exists a set [Formula: see text] such that [Formula: see text] and [Formula: see text]. The minimum cardinality of a [Formula: see text]-DRD set of a graph [Formula: see text] is called the [Formula: see text]-part degree r...
International Journal of Wireless & Mobile Networks (IJWMN), 2011
In this paper, a new multi-hop weighted clustering procedure is proposed for homogeneous Mobile A... more In this paper, a new multi-hop weighted clustering procedure is proposed for homogeneous Mobile Ad hoc networks. The algorithm generates double star embedded non-overlapping cluster structures, where each cluster is managed by a leader node and a substitute for the leader node (in case of failure of leader node). The weight of a node is a linear combination of six different graph theoretic parameters which deal with the communication capability of a node both in terms of quality and quantity, the relative closeness relationship between network nodes and the maximum and average distance traversed by a node for effective communication. This paper deals with the design and analysis of the algorithm and some of the graph theoretic/structural properties of the clusters obtained are also discussed.
In this paper, we propose a new distributed weighted clustering algorithm for MANETs by introduci... more In this paper, we propose a new distributed weighted clustering algorithm for MANETs by introducing a new graph parameter called strong degree defined based on the quality of neighbors of a node. The proposed algorithm is a cluster-head based algorithm. The ...
In this paper, we propose a new multi-parameter weight based double star embedded clustering algo... more In this paper, we propose a new multi-parameter weight based double star embedded clustering algorithm for MANETs. The weight of a node is a linear combination of six different graph theoretic parameters which deal with the communication capability of a node both ...
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Papers by Senthil Thilak