*Ferdinand Jamil (Mindanao State University-Iligan Institute of Technology (MSU-IIT))

Let $G$ be a finite connected undirected graph with no loops and multiple edges. For two vertices $u$ and $v$ of $G$, a $u$-$v$ geodesic is any shortest path joining $u$ and $v$. The closed geodetic interval $I_G[u,v]$ consists of all vertices of $G$ lying on any $u$-$v$ geodesic. For $S\subseteq V(G)$, $V(G)$ being the vertex set of $G$, $S$ is a geodetic set in $G$ if $\cup_{u,v\in S}I_G[u,v]=V(G)$.
Vertices $u$ and $v$ of $G$ are neighbors if $u$ and $v$ are adjacent. The closed neighborhood $N_G[v]$ of vertex $v$ consists of $v$ and all neighbors of $v$. For $S\subseteq V(G)$, $S$ is a dominating set in $G$ if $\cup_{u\in S}N_G[u] = V(G)$. A geodetic dominating set in $G$ is any geodetic set in $G$ which is a geodetic set and at the same time a dominating set in $G$. This plenary talk concerns on the characterizations of the geodetic dominating sets, particularly in graphs resulting from some binary graph operations.