Application of graph theory in domination of graphs

Box , Jeddah , Saudi Arabia. Fuzzy graphs FGs , broadly known as fuzzy incidence graphs FIGs , have been recognized as being an effective tool to tackle real-world problems in which vague data and information are essential. Dominating sets DSs have multiple applications in diverse areas of life. In wireless networking, DSs are being used to find efficient routes with ad hoc mobile networks. In this paper, we extend the concept of domination of FGs to the FIGs and show some of their important properties. We propose the idea of order, size, and domination in FIGs.
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Dominating set

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Dominating set - Wikipedia

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. Dissertation Director: Fred S. Many different types of domination have been researched extensively. This dissertation explores some new variations and applications of dominating sets. We first introduce the concept of Roman domination. A Roman dominating function… Expand.
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APPLICATIONS AND VARIATIONS OF DOMINATION IN GRAPHS

Figures a — c on the right show three examples of dominating sets for a graph. In each example, each white vertex is adjacent to at least one red vertex, and it is said that the white vertex is dominated by the red vertex. The domination number of this graph is 2: the examples b and c show that there is a dominating set with 2 vertices, and it can be checked that there is no dominating set with only 1 vertex for this graph.
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