2025/06/13 by Deepak M. Bakal, Bakal, Deepak M., S. A. Mane +1
Computer Science · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2506.11865
openalex publication_date 2025/06/13 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
In this paper, we obtain the exact values of several domination parameters for the direct product of a complete graph with a path or a cycle. Specifically, we determine the domination number, independent domination number, [1,2]-domination number, secure domination number, and 2-domination number for this family of graphs. We show that, in these graphs, the independent domination number and the [1,2]-domination number coincide with the domination number, while the secure domination number coincides with the 2-domination number. Additionally, as a consequence of our findings, we provide counterexamples to disprove some erroneous results in the literature.