Dimensi Metrik Ketetanggaan Lokal pada Graf Hasil Operasi Korona G odot P_3 dan G odot S_4 - Alfin Nabila Taufik; Dafik Dafik; Rafiantika Megahnia Prihandini; Ridho Alfarisi (CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS, 2020)
There are variant of the metric dimensions in graph theory, one of them is a local adjacency metric dimension. Let $W\subset V(G)$ with $W=\{w_1,w_2,…,w_k\}$, the representation of the vertex $V\in V(G)$, $r_A(v|W)=(d_A(v,w_1),d_A(v,w_2),…,d_A(v,w_k))$ with $ d_ A (v, w) $= $ 0 $ if $ v = w $, $ d_ A (v, w) $= $ 1 $ if $ v$ adjacent to $w $, and $ d_ A (v, w) $ =$ 2 $ if $ v $ does not adjacent to $ w $. If every two adjacent vertices $ v_1 $, $ v_2 \in V (G) $, $ r_ A (v_1 | W) ≠ r_ A (v_2 | W) $, then $W$ is the minimum cardinality of the local adjacency metric dimension. The minimum cardinality of $W$ is called the local adjacency metric dimension number, denoted by $ \dim_{(A, l)} (G) $. In this paper, we have found the local adjacency metric dimension of corona product of special graphs, namely the $ L_n \odot {P_3} $ graph, $ S_n \odot {P_3} $ graph, $ C_n \odot {P_3} $ graph, $ P_n \odot {S_4} $ graph, and the graph $ L_n \odot {S_4} $.