2022/11/04 by Sarah Anderson, Boštjan Brešar, Anderson, Sarah +7
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2211.02395
openalex publication_date 2022/11/04 · openalex created_date 2023/02/15 · openalex updated_date 2026/07/28
The orientable domination number, \rm DOM(G), of a graph G is the largest domination number over all orientations of G. In this paper, \rm DOM is studied on different product graphs and related graph operations. The orientable domination number of arbitrary corona products is determined, while sharp lower and upper bounds are proved for Cartesian and lexicographic products. A result of Chartrand et al. from 1996 is extended by establishing the values of \rm DOM(Kn1,n2,n3) for arbitrary positive integers n1,n2 and n3. While considering the orientable domination number of lexicographic product graphs, we answer in the negative a question concerning domination and packing numbers in acyclic digraphs posed in [Domination in digraphs and their direct and Cartesian products, J. Graph Theory 99 (2022) 359-377].