Domination in graphoidally covered graphs: Least-kernel graphoidal graphs-II

Peer review under responsibility of Kalasalingam University.

Figures & data

Fig. 1 A graphoidally covered graph.

Fig. 2 $(G,\Psi )$, where $\Psi =\left\{(u,v)\right\}\cup \{(u,v_i,u_i):i\in \mathbb{N}\}\cup \{(v,v_i):i\in \mathbb{N}\}$, is ${\gamma }_{\Psi }\left(G\right)$-definable but not ${\gamma }_{i\Psi }\left(G\right)$-definable and ${\gamma }_{\Psi }\left(G\right)=\{u,v\}$.

Fig. 3 Example of a graph which is not an LKG graph.

Fig. 4 An LKG cover $\Psi$ of $T$ obtained by spider decomposition with initial root $u_0$. Here $D=\{u_0,u_1,u_2,w_0,w_1,w_2,w_3\}$ is a ${\gamma }_{\Psi }\left(T\right)\left({\gamma }_{i\Psi }\left(T\right)\right)$-set.

Fig. 5 A cactus.

Fig. 6 LKG covers of two different graphs constructed using the technique described in case 1 and case 2.