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671  Articles
1 of 68 pages  |  10  records  |  more records»
A paired dominating set of a graph G is a dominating set whose induced subgraph has a perfect matching. The paired domination number ?pr(G) of G is the minimum cardinality of a paired dominating set. A paired dominating set&n... see more

Given a simple graph G=(V,E) with maximum degree ?. Let (V0, V1, V2) be an ordered partition of V, where Vi = {v ? V : f(v)=i} for i = 0, 1 and V2 = {v ? V : f(v)=2}. A function f : V ? {0, 1, …, ??/2?+1} ... see more

We investigate the problem of simultaneously dominating all spanning trees of a given graph. We prove that on 2-connected graphs, a subset of the vertices dominates all spanning trees of the graph if and only if it is a vertex cover. Using this fact we pr... see more

Efficient routing between nodes is the most important challenge in a Mobile Ad Hoc Network (MANET). A Connected Dominating Set (CDS) acts as a virtual backbone for routing in a MANET. Hence, the construction of CDS based on the need and its application pl... see more

We consider a set D ? V(G) which dominate G and for every two distinct vertices x, y ? V(G) \ D, the open neighborhood of x and y in D are different. The minimum cardinal... see more

Recently we introduced the concept of minimum dominating energy[21]. Motivatedby this paper,we introduced the concept of minimum dominating distance energyEDd(G) of a graph G and computed minimum dominating distance energies of a Stargraph,Complete graph,... see more

A set D of vertices in a graph G = (V (G), E(G)) is an open neighborhood locating-dominating set (OLD-set) for G if for every two vertices u, v of V (G) the sets N(u) n D and N(v) n D are non-empty and different. The open neighborhood locating-dominating ... see more

Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its neighbourhood within the d... see more

We study the relationship between the eternal domination number of a graph and its clique cove-ring number using both large-scale computation and analytic methods. In doing so, we answer two open questions of Klostermeyer and Mynhardt. We show that the sm... see more

1 of 68 pages  |  10  records  |  more records»