Dimensi Metrik Sisi Pada Beberapa Graf Unicyclic - Bayu Aprilianto; Dafik Dafik; Ermita Rizki Albirri (CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS, 2020)
All the graphs in this paper are connected graphs and $d(e,v)$ is the length of the shortest path between $e=uv$ and $v$. Let $G=(V,E)$ where $V(G)$ is a set of vertex from graph $G$ while $E(G)$ is a set of edge from graph $G$. The edge metric dimension is a topic that is closely related to the cardinality of the distance of each edge on the graph $G$ with respect to the resolving set $W$ which is denoted by $dim_E(G)$. Let if the subset of vertex $W=\{w_1,w_2,w_3,...,$ $w_k\}$, then the representation of the distance of the $uv$ edge to the set of differences is k-tuple $r(uv|W)=(d(uv,w_1),d(uv,w_2),d(uv,w_3),...,d(uv,w_k)$. A unicyclic graph is one that only has exactly one cycle. In this paper, we will study edge metric dimensions on some families of unicyclic graphs.