Domination in graph theory

Many variants of dominating sets are available in the existing literature. The present work is intended to discuss the problem of the third kind in the context of edge domination in graphs. A dominating set is called a minimal dominating set MDS if no proper subset of is a dominating set. Contact the MathWorld Team. Glashow have Erdos number 2, the computational biologist L. Let the switched vertex be the apex vertex of. First let us choose u 1.
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Edge Domination in Some Path and Cycle Related Graphs

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International Scholarly Research Notices

Thus, being a minimal dominating set with minimum cardinality is a -set of which implies that. This is an open-access article distributed under the terms of the Creative Commons Attribution License. We have found that the number of sets of category A is 21; that of category B is 21; and that of category C is 2. The RNPCG network is a description of the paths among the participants where transfer of knowledge happens in joint research work. But, from the nature of graph, we can observe that each of at most distinct edges of can dominate seven distinct edges including itself and each of the remaining edges can dominate less than six edges of.
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Distance 2-Domination in Prisms of Graphs : Discussiones Mathematicae Graph Theory

The open neighborhood of is the set of vertices adjacent to , and the set is the closed neighborhood of. This happens under the limitation just observed. Stochastic models for the web graph. Let be the vertices of the first copy of and the vertices of the second copy of. If dominating sets with minimum order possess much smaller order than the size of the network then that brings down the cost of computation of identifying the elites. In Erdos collaboration graph that we consider below the vertex represented by Erdos is the central vertex.
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In social networks, One can consider the assumption that dominating sets with minimum order contain agents that strongly influence the rest of the members in the network. Thus, we have the following proposition:. The RNPCG network is a description of the paths among the participants where transfer of knowledge happens in joint research work. We begin with simple, finite, connected, and undirected graph of order. Now, the edge sets and are clearly the minimal edge dominating sets of and , respectively, with minimum cardinality among all minimal edge dominating sets of.
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