Speaker
Marko Jakovac
(University of Maribor)
Description
The distance between two vertices $u,v \in V(G)$, denoted by $d(u,v)$, is the length of a shortest
$u,v$-path in graph $G$. The distance between a vertex $v \in V(G)$ and a subset $P \subseteq V(G)$
is defined as $\min\{d(v,x) \, | \, x \in P \}$, and is denoted by $d(v,P)$. An ordered
partition $\{P_1,P_2,\ldots , P_t\}$ of vertices of a graph $G$, is a resolving partition of
$G$, if all the distance vectors $(d(v,P_1),d(v,P_2),\ldots ,d(v,P_t))$ are different. The
partition dimension of $G$ is the minimum number of sets in any resolving partition of
$G$. Some results on the partition dimension of strong product graphs and Cartesian product graphs
will be presented.
Joint work with Ismael Gonz\'alez Yero, Dorota Kuziak and Andrej Taranenko.
Primary author
Marko Jakovac
(University of Maribor)
