Total Roman domination edge-critical graphs
Chloe Lampman, Christina M. Mynhardt, Shannon Ogden · Involve a Journal of Mathematics · 2019
A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} such that every vertex v with f (v) = 0 is adjacent to some vertex u with f (u) = 2, and the subgraph of G induced by the set of all vertices w such that f (wWe present some basic results on γ tR -edge-critical graphs and characterize certain classes of γ tR -edgecritical graphs.In addition, we show that, when k is small, there is a connection between k-γ tR -edge-critical graphs and graphs which are critical with respect to the domination and total domination numbers. MSC2010: 05C69.