Graphs whose vertex set can be partitioned into a total dominating set and an independent dominating set (Q6545237)

A graph \(G\) whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. In this paper, the authors prove that complete multipartite graphs, maximal outerplanar graphs, and claw-free graphs with minimum degree at least 3 are TI-graphs and give constructions that yield infinite families of graphs that are TI-graphs, as well as constructions that yield infinite families of graphs that are not TI-graphs. They study regular graphs and cubic graphs that are TI-graphs. Among other results, it is proved that all toroidal graphs are TI-graphs. An open problem concludes the paper.