Advances and Applications in Discrete Mathematics
Volume 19, Issue 3, Pages 171 - 182
(July 2018) http://dx.doi.org/10.17654/AADMJul2018_171_182 |
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CONNECTED dr-POWER DOMINATING SETS IN GRAPHS
Isagani S. Cabahug, Jr. and Sergio R. Canoy, Jr.
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Abstract: Let G be a simple graph. A set is called a connected dr-power dominating set of Gif it is a dr-power dominating set and the induced subgraph of P, denoted by is connected. The minimum cardinality of a connected dr-power dominating set Pof a graph G, denoted by is the connected dr-power domination number of G. This parameter is at most equal to the connected domination number of a graph G. In this paper, we investigate the connected dr-power dominating sets in a graph. It is shown that any two positive integers aand b, where are realizable as the connected dr-power domination number and connected domination number, respectively. Connected dr-power dominating sets in the join, corona, and lexicographic product of graphs are also characterized. |
Keywords and phrases: connected domination, dr-power domination, directly observed vertex, remotely observed vertex, directly observed edge, remotely observed edge, connected dr power domination. |
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