Secure domination of honeycomb networks

M. R. Chithra () and Manju K. Menon ()
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M. R. Chithra: Amrita School of Arts and Sciences, Kochi Amrita Vishwa Vidyapeetham
Manju K. Menon: St. Paul’s College

Journal of Combinatorial Optimization, 2020, vol. 40, issue 1, No 7, 98-109

Abstract: Abstract The topological structure of a network can be described by a connected graph $$G = (V, E)$$G=(V,E) where V(G) is a set of nodes to be connected and E(G) is a set of direct communication links between the nodes. A physical connection between the different components of a parallel system is provided by an interconnection network. Many graph theoretic parameters are used to study the efficiency and reliability of an interconnection network. A set $$S \subseteq V(G)$$S⊆V(G) is said to be secure if the security condition, for every $$X \subseteq S$$X⊆S, $$\left| N[X] \cap S\right| \ge \left| N[X] - S\right| $$N[X]∩S≥N[X]-S holds. Now, a set $$S \subseteq V(G)$$S⊆V(G) is secure dominating, if it is both secure and dominating. The secure domination number of G, is the minimum cardinality of a secure dominating set in G. In the current era, security is definitely a desirable property for the interconnection networks and hence these type of study has wide applications. In this paper, we have studied the security number and secure domination number of Honeycomb Networks.

Keywords: Domination; Secure domination; Honeycomb networks; 05C69; 05C99 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10878-020-00570-8

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