Article: On 2-domination number in certain octahedral networks Journal: International Journal of Networking and Virtual Organisations (IJNVO) 2022 Vol.27 No.3 pp.251 - 266 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. Inderscience Publishers - linking academia, business and industry through research

Title: On 2-domination number in certain octahedral networks

Authors: S. Arulanand; R. Sundara Rajan; S. Prabhu

Addresses: Department of Mathematics, Hindustan Institute of Technology and Science, Chennai – 603 103, India ' Department of Mathematics, Hindustan Institute of Technology and Science, Chennai – 603 103, India ' Department of Mathematics, Rajalakshmi Engineering College, Thandalam – 602 105, India

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.

Keywords: domination; 2-domination; octahedral network.

DOI: 10.1504/IJNVO.2022.128463

International Journal of Networking and Virtual Organisations, 2022 Vol.27 No.3, pp.251 - 266

Received: 14 Mar 2022
Accepted: 30 Oct 2022
Published online: 23 Jan 2023 *

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Title: On 2-domination number in certain octahedral networks

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