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Total domination and minimal total domination polynomial of H-join graphs
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Total domination and minimal total domination polynomial of H-join graphs
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Journal Article
Total domination and minimal total domination polynomial of H-join graphs
2025
Overview
Let H be a connected labeled graph. In this article, we characterize all the total dominating sets and the minimal total dominating sets of H-join graphs. Consequently, we compute the (multivariate) total domination polynomial and the (multivariate) minimal total domination polynomial of H-join graphs. We also compute the total domination number of H-join graphs. Finally, as an illustration, we calculate the total domination polynomial and the minimal total domination polynomial of the join of graphs, multipartite graphs, Kn-join graphs, Kn1,...,nm-join graphs, the corona product of graphs and the windmill graphs.
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