On 2-domination number in certain octahedral networks
by S. Arulanand; R. Sundara Rajan; S. Prabhu
International Journal of Networking and Virtual Organisations (IJNVO), Vol. 27, No. 3, 2022

Abstract: Fault tolerance is the characteristic that facilitates a system to function when some of its components fail. Thus, developing a fault-tolerant system can respond quickly to threats and mitigate operations spontaneously. Fault tolerance and graph theory form a unique and highly desirable combination with the potential to design diverse fault-tolerant networks at the lowest possible cost. This is achieved using a mathematical framework 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. The minimum number of elements of a dominating set is called the domination number of that network. If any node in the network has a minimum of two neighbours in the set, then the set is called a 2-dominating set. The minimum number of elements of such a set is called the 2-domination number. In this paper, the 2-domination numbers for various octahedral networks like n-dimensional octahedron, n-dimensional dominated octahedron, and n-dimensional rectangular octahedron of type I and II are computed. The leading actual world application of the 2-dominating set is fault tolerance. The motivation for our work is how the fault tolerance system is applicable in the octahedral network.

Online publication date: Mon, 23-Jan-2023

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