2 problems

Let $G$ be a simple graph of order $n$. A graph is $3_t$-critical if its total domination number is $3$ and adding an edge between any nonadjacent vertices lowers its total dominat…

Let $G=(V,E)$ be a simple graph, let … be its total domination polynomial, where $n$ is the order of $G$ and $d_t(G,i)$ counts the total dominating sets of cardinality $i$. A root…