S. Bera

On graphs with equal domination and total domination numbers

For a graph $G$ without isolated vertices, $\gamma(G)\le\gamma_t(G)\le 2\gamma(G)$. While graphs attaining $\gamma(G)=\gamma_t(G)$ have been studied extensively, a complete structural description in the smallest nontrivial case $\gamma(G)=2$ has remained open. We resolve this case according to girth. When $g(G)\ne 3$,...