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Protection of Complete Multipartite Graphs |
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S Benecke1, PJP Grobler2 & JH van Vuuren3
Abstract
The notion of higher order domination in graphs has been studied in the literature and may be categorised as so-called finite higher order domination and infinite higher order domination. The former concept concerns the protection of a graph against a finite number of attacks, while the latter caters for an infinite number of attacks. Although the infinite order domination parameters were established for the complete multipartite graph, only the secure finite order parameters were resolved, and only for the complete bipartite case. In this paper, both the smart and foolproof versions of the secure and weak Roman higher order domination parameters are fully established for the complete multipartite graph.
An electronic version of the complete paper may be obtained here: [ps] [pdf].
Affiliations
1
Department of Applied Mathematics, Stellenbosch University, Private Bag X1, Matieland, 7602, Republic of South Africa, email: sbenecke@dip.sun.ac.za