Total domination number of middle graphs
| Main Authors: | Kazemnejad, Farshad; Faculty of Basic Sciences, Department of Mathematics, Ilam University, Iran, Pahlavsay, Behnaz; Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Japan, Palezzato, Elisa; Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Japan, Torielli, Michele; Department of Mathematics, GI-CoRE GSB, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Japan |
|---|---|
| Other Authors: | JSPS |
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2022
|
| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1227 https://www.ejgta.org/index.php/ejgta/article/view/1227/pdf_219 |
Daftar Isi:
- A total dominating set of a graph G with no isolated vertices is a subset S of the vertex set such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set. In this paper, we study the total domination number of middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph. We also compute the total domination number of the middle graph of some known families of graphs explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the total domination number of middle graphs.