[1,2]-Domination in generalized Petersen graphs
نویسندگان
چکیده
منابع مشابه
On Power Domination of Generalized Petersen Graphs
The power dominating problem is a variation of the classical domination problem in graphs. Electricity company use phase measurement units (PMUs) to produce the measuring data of a system, and use these data to estimate states of the system. Because of the high cost of PMUs, minimizing the number of PMUs on a system is an important problem for electricity companies. This problem can be modeled ...
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A set S of vertices in a graph G is a double total dominating set, abbreviated DTDS, of G if every vertex of G is adjacent to least two vertices in S. The minimum cardinality of a DTDS of G is the double total domination number of G. In this paper, we study the DTDS of the generalized Petersen graphs. Mathematics Subject Classification: 05C35
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Generalized Petersen graphs are an important class of commonly used interconnection networks and have been studied . The total domination number of generalized Petersen graphs P(m,2) is obtained in this paper.
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A set S of vertices is defined to be a power dominating set (PDS) of a graph G if every vertex and every edge in G can be monitored by the set S according to a set of rules for power system monitoring. The minimum cardinality of a PDS of G is its power domination number. In this article, we find upper bounds for the power domination number of some families of Cartesian products of graphs: the c...
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Assume we have a set of k colors and we assign an arbitrary subset of these colors to each vertex of a graph G. If we require that each vertex to which an empty set is assigned has in its neighborhood all k colors, then this assignment is called a k-rainbow dominating function of G. The corresponding invariant γrk(G), which is the minimum sum of numbers of assigned colors over all vertices of G...
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ژورنال
عنوان ژورنال: Discrete Mathematics, Algorithms and Applications
سال: 2019
ISSN: 1793-8309,1793-8317
DOI: 10.1142/s1793830919500587