Advances and Applications in Discrete Mathematics
Volume 22, Issue 1, Pages 103 - 115
(September 2019) http://dx.doi.org/10.17654/DM022010103 |
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ON CONNECTED TOTAL DOMINATING SETS AND CONNECTED TOTAL DOMINATION POLYNOMIAL OF CORONA GRAPHS
Giovannie M. Entero and Ariel C. Pedrano
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Abstract: A set is a connected total dominating set of the graph G if and only if S admits the following three conditions: a dominating set of graph G, that is for every vertex in is adjacent to at least one vertex in S, equivalently a total dominating set of graph G, that is for every vertex in there exists a vertex such that v is adjacent to u, equivalently and the induced subgraph by the total dominating set S of graph G is connected. The connected total domination number of graph G is the minimum cardinality taken over all connected total dominating sets of graph G. The connected total domination polynomial of the graph G is defined as where is the order of graph G, is the connected total domination number of graph G, and where is the family of connected total dominating sets of graph G.
In this paper, we obtain the following results: the connected total domination number of the corona graph the connected total dominating sets of the corona graph and the connected total domination polynomial of the corona graph |
Keywords and phrases: connected total dominating sets, connected total domination number, connected total domination polynomial, corona graphs.
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