Misalkan G=(V(G),E(G)) adalah graf dengan himpunan simpul V(G) dan himpunan busur E(G). Misalkan f∶E→{1,2,… ,|E(G)|} suatu pemetaan bijektif. Untuk setiap simpul u ∈V(G), bobot dari simpul u adalah w(u)=∑_(e∈E(u))▒〖f(e)〗, dimana E(u) adalah himpunan busur yang bersisian dengan u. Jika untuk setiap u, v∈V(G) berlaku w(u)≠w(v) maka f disebut pelabelan antiajaib dari G. Selanjutnya, f disebut pelabelan antiajaib lokal jika untuk u,v∈V(G) dengan u dan v  bertetangga, maka w(u)≠w(v). Pelabelan antiajaib lokal memunculkan sifat pewarnaan simpul dimana simpul u diberi warna berdasar bobot w(u). Bilangan kromatik antiajaib lokal graf G, dinotasikan X_la (G) adalah banyaknya warna minimum pada pelabelan simpul yang ditimbulkan oleh pelabelan antiajaib lokal. Operasi perkalian korona dari dua graf G dan H, dinotasikan dengan G∘H, adalah graf yang dibentuk dari graf G dan graf H dengan menyalin graf H sebanyak |V(G)|, sebut H_1,H_2,…,H_|V(G)| selanjutnya ditambahkan busur sehingga semua simpul di H_i bertetangga dengan simpul x_i di G, untuk 1 ≤ i ≤ |G|. Tesis ini membahas bilangan kromatik antiajaib lokal graf perkalian korona dua lintasan, yaitu〖 X〗_la (P_n∘P_k ), dimana  k=2,3,5. Hasil penelitian menunjukkan bahwa bilangan kromatik pelabelan simpul antiajaib lokal, 〖 X〗_la (P_n∘P_k ), untuk  k=2,3,5 adalah  X_la (P_n∘P_2 )=6 untuk n≥4 ,〖 X〗_la (P_n∘P_3 )=6,untuk n≥4 and X_la (P_n∘P_5 )=7, untuk n ≥5.

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Enable GingerLet G=(V,E) be a graph with vertex set V and edge set E. Let f:E→{1,2,…,|E|} be a bijection map. For each vertex u ∈V(G), the weigh of vertex u is w(u)=∑_(e∈E(u))▒〖f(e)〗, where E(u) is the set of edges incident to u. If for each u,v∈V(G), w(u)≠w(v) then f is called antimagic labelling of G. Furthermore, f is called antimagic labelling of G if for any two adjacent vertices u,v∈V(G), then w(u)≠w(v). The local antimagic labeling induces a proper vertex coloring of G where the vertex v is assigned the color (vertex sum) w(v).  The local antimagic chromatic number, denoted X_la (G), is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. Let G and H be two graphs. The corona product graph G∘H is obtained by taking one copy of  G along with |V(G)|  copies of H, and via putting extra edges making the ith vertex of G adjacent to every vertex of the ith copy of H, where 1≤i ≤|V(G)|. This thesis discusses the local antimagic chromatic number of corona product graph two paths,〖 X〗_la (P_n∘P_k ), where k=2,3,5. The result showed that the chromatic number of local antimagic vertex coloring P_n∘P_k,for k=2,3,5 are X_la (P_n∘P_2 )=6 for n≥4,〖 X〗_la (P_n∘P_3 )=6,for n≥4,X_la (P_n∘P_5 )=7, for n≥5.
 

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