Advances and Applications in Discrete Mathematics
Volume 27, Issue 1, Pages 147 - 155
(May 2021) http://dx.doi.org/10.17654/DM027010147 |
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ON CONNECTED TOTAL DOMINATION POLYNOMIAL OF SOME LEXICOGRAPHIC PRODUCT 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: a dominating set of G, that is for every vertex in is adjacent to at least one vertex in S, equivalently, a total dominating set of 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 G which is connected. The connected total domination number of the graph G is the minimum cardinality taken over all connected total dominating sets of G. The connected total domination polynomial of the graph G is defined as where is the order of G, is the connected total domination number of G, and where is the family of connected total dominating sets of G.
In this paper, we obtain the connected total domination number of the lexicographic graph the connected total dominating sets of the lexicographic graph and the connected total domination polynomial of the lexicographic graph |
Keywords and phrases: connected total dominating sets, connected total domination number, connected total domination polynomial, lexicographic product graphs.
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