Dimensi Metrik Ketetanggaan Lokal pada Graf Hasil Operasi Korona G odot P_3 dan G odot S_4

Abstract

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 $W=\{w_1,w_2,\dots,w_k\}$, the representation of the vertex $V\in V(G)$, $r_A(v|W)=(d_A(v,w_1),d_A(v,w_2),\dots,d_A(v,w_k))$ 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) eq 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} $.