Advances and Applications in Discrete Mathematics
Volume 25, Issue 2, Pages 267 - 274
(November 2020) http://dx.doi.org/10.17654/DM025020267 |
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WEAKLY CONNECTED TOTAL DOMINATION CRITICAL GRAPHS
Elsie P. Sandueta
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Abstract: A subset X of V(G) is a dominating set of G if for every there exists such that that is, It is a total dominating set if A dominating set S of V(G) is a weakly connected dominating set of G if the subgraph weakly induced by S is connected. A total dominating set S of V(G) is a weakly connected total dominating set of G if is connected. The weakly connected domination number (weakly connected total domination number of G is the smallest cardinality of a weakly connected dominating (resp., weakly connected total dominating) set of G. A graph is said to be weakly connected total domination critical, -critical if for each with x not adjacent to y, Hence, G is k--critical if and for each
In this paper, we characterize weakly connected total domination critical graphs and give some classes of graphs which are weakly connected total domination critical. |
Keywords and phrases: domination, weakly connected total domination, critical graphs, networks.
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