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 subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...

A virtual backbone of a wireless network is a connected subset of nodes responsible for routing messages in the network. A node in the subset is likely to be exhausted much faster than the others due to its heavy duties. This situation can be more aggravated if the node uses higher communication power to form the virtual backbone. In this paper, we introduce the minimum total communication powe...

Let G = (V , E) be a graph. A subset D ⊆ V is a dominating set if every vertex not in D is adjacent to a vertex in D. A dominating set D is called a total dominating set if every vertex in D is adjacent to a vertex in D. The domination (resp. total domination) number of G is the smallest cardinality of a dominating (resp. total dominating) set of G. The bondage (resp. total bondage) number of a...

A reliable and efficient broadcast procedure is essential for the Vehicular Ad Hoc Networks (VANET) because a major portion of services need to broadcast the messages to the vehicles within a certain area of interest, The broadcasting should ensure a minimum number of transmissions and also should guarantee delivery. Several such broadcasting protocols have been implemented till date, but inter...

We present the first polynomial time algorithms for solving the NPcomplete graph problems DOMINATING SET and TOTAL DOMINATING SET when restricted to asteroidal triple-free graphs. We also present algorithms to compute a minimum cardinality dominating set and a minimum cardinality total dominating set on a large superclass of the asteroidal triple-free graphs, called DDP-graphs. These algorithms...

For a given connected graphG= (V ,E), a setDtr ⊆ V (G) is a total restrained dominating set if it is dominating and both 〈Dtr〉 and 〈V (G)−Dtr〉 do not contain isolate vertices. The cardinality of the minimum total restrained dominating set in G is the total restrained domination number and is denoted by tr(G). In this paper we characterize the trees with equal total and total restrained dominati...

This paper investigates a tuple-oriented approach to tabulation. In this approach solutions to a call are stored and computed one at a time, which results in tables contain incomplete sets of solutions. Since the answers stored in the tables are partial sets of solutions to a call, a subgoal that is an instance of a stored call can require an answer that is not among the stored solutions. Conse...

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...