- Tytuł:
- Total Domination in Generalized Prisms and a New Domination Invariant
- Autorzy:
- Tepeh, Aleksandra
- Powiązania:
- https://bibliotekanauki.pl/articles/32222717.pdf
- Data publikacji:
- 2021-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
domination
k -rainbow total domination
total domination - Opis:
- In this paper we complement recent studies on the total domination of prisms by considering generalized prisms, i.e., Cartesian products of an arbitrary graph and a complete graph. By introducing a new domination invariant on a graph G, called the k-rainbow total domination number and denoted by γkrt(G), it is shown that the problem of finding the total domination number of a generalized prism G □ Kk is equivalent to an optimization problem of assigning subsets of {1, 2, . . ., k} to vertices of G. Various properties of the new domination invariant are presented, including, inter alia, that γkrt(G) = n for a nontrivial graph G of order n as soon as k ≥ 2Δ(G). To prove the mentioned result as well as the closed formulas for the k-rainbow total domination number of paths and cycles for every k, a new weight-redistribution method is introduced, which serves as an efficient tool for establishing a lower bound for a domination invariant.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1165-1178
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł