2-domination number for special classes of hypercubes, enhanced hypercubes and Knödel graphs Online publication date: Thu, 23-Nov-2023
by S. Arulanand; R. Sundara Rajan; S. Prabhu
International Journal of Networking and Virtual Organisations (IJNVO), Vol. 29, No. 2, 2023
Abstract: The system is fault-tolerant if, in the case that just one of the previously employed units fails, a different chain of units is utilised in its place. Because they provide the best fault tolerance, cycle-related graphs are employed in network analysis, periodic scheduling, and surface reconstruction. This can be achieved through a mathematical concept called domination. In a graph, each node has a minimum of one neighbour in a set, and then the set is called a dominating set of a network. A dominating set with the least cardinality is the domination number of the network. In this paper, we obtain the 2-domination number of some special classes of hypercubes, enhanced hypercubes, and Knödel graphs proving that the lower bound obtained in Fink and Jacobson (1985). quite precise, and also we prove that the time complexity of the 2-domination problem for the above graphs are linear.
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