2020/07/26 by Vladimir Samodivkin, Samodivkin, Vladimir · 1 citation
Computer Science · Mathematics · #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2007.13095
openalex publication_date 2020/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we begin an exploration of several domination-related\nparameters (among which are the total, restrained, total restrained, paired,\nouter connected and\n total outer connected domination numbers) in the generalized lexicographic\nproduct (GLP for short) of graphs. We prove that for each GLP of graphs there\nexist several equality chains containing these parameters. Some known results\non standard lexicographic product of two graphs are generalized or/and\nextended. We also obtain results on well \μ-dominated GLP of graphs, where\n\μ stands for any of the above mentioned domination parameters. In\nparticular, we present a characterization of well \μ-dominated GLP of graphs\nin the cases when \μ is the domination number or the total domination\nnumber.\n