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INDEPENDENT SEMITOTAL DOMINATION IN THE LEXICOGRAPHIC PRODUCT OF GRAPHS
Keywords:
independent semitotal domination, independent domination, lexicographic product of graphsDOI:
https://doi.org/10.17654/0974165823050Abstract
Consider a connected noncomplete graph $G$ with at least 3 vertices. If $W \subseteq V(G)$ is independent and dominates $G$ such that every element of $W$ is exactly of distance 2 from another element of $W$, then $W$ is an independent semitotal dominating set of $G$, abbreviated $I S T d$-set of $G$. The parameter $\gamma_{i t 2}(G)$ represents the lowest cardinality of an ISTd-set of $G$. In this paper, we consider the composition $G[H]$ of $G$ by $H$, where $G$ is a connected noncomplete graph and $H$ is any connected graph, and obtain its independent semitotal domination number.
Received: May 7, 2023
Revised: May 27, 2023
Accepted: June 10, 2023
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