THE L(3,2,1) LABELING OF SOME GRAPHS - LAPENANGGA PUTRA (NIM: 20116029), GANESHA
Let G=(V,E) be a nontrivial and connected graph. The L(3,2,1) labeling of graph G is a function f:V→ N∪{0} such that |f(u)-f(v)|≥ 3 for every u,v∈ V with d(u,v)=1, |f(u)-f(v)|≥ 2 for every u,v∈ V with d(u,v)=2, and |f(u)-f(v)|≥ 1 for every u,v∈ V with d(u,v)=3. For non-negative integer k, a k-L(3,2,1) labeling is an L(3,2,1) labeling such that no label is greater than k. The L(3,2,1) number of G, denoted by λ_3,2,1 (G), is the smallest number k such that G has a k-L(3,2,1) labeling. Let G and H be a nontrivial and connected graphs. The Cartesian product of graph G and H, denoted by G□ H, is a graph with vertex set V(G□H)=V(G)ÃƒÂ— V(H) such that (u_1,v_1) and (u_2,v_2) adjacent if and only if u_1=u_2 and v_1 v_2∈ E(H) or v_1=v_2 and u_1 u_2∈ E(G). In this thesis, we determine the λ_3,2,1 number of a Jahangir graph, caterpillar graph and Cartesian product of a uniform caterpillar graph and path.