PELABELAN KN-AJAIB SUPER DAN (A;D)-KN-ANTIAJAIB SUPER PADA GRAF LENGKAP KN KORONA GRAF LENGKAP KN,1

• Main Author: NANDA MARDANI, ZAGALO
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/19759
• Institution: Institut Teknologi Bandung

Let G = (V (G);E(G)) be a graph and H be a subgraph of G. Graph G admits H-covering, if every edge in G belongs to subgraph of G isomorphic to H. An H-magic labelling of G which admits H-covering is a bijection f : V (G) [ E(G) ! f1; 2; :::; jV (G)j+jE(G)jg such that there is a magic constant C satisfies wt(Hi) = P v2V (Hi) f(v) + P e2E(Hi) f(e) = C for every subgraphs Hi isomorphic to H. When f(V (G)) = f1; 2; :::; jV (G)jg, the labelling f is called super H-magic. An (a; d)-H-antimagic labelling of G which admits H-covering is a bijection g : V (G) [ E(G) ! f1; 2; :::; jV (G)j+jE(G)jg such that the H-weights wt(Hi) = P v2V (Hi) g(v) + P e2E(Hi) g(e) constitute an arithmetic progression a; a+d; a+2d; :::; a+(t????1)d where a and d are some positive integers and t is the number of subgraphs of G isomorphic to H. When g(V (G)) = f1; 2; :::; jV (G)jg, the labelling g is called super (a; d)-H-antimagic. A graph which has a super H- magic labelling and a super (a; d)-H-antimagic labelling is called super H-magic and super (a; d)-H-antimagic, respectively. Graph G1 corona graph G2, denoted by G1 G2, is a graph obtained by taking one copy of G1 which has n-vertices and n-copies of G2 and then appending edges which join every ith-vertex of G1 to every vertex in the ith-copy of G2. In this paper, we consider a complete graph Kn corona a complete graph Kn????1 for any n 3. We prove that Kn Kn????1 is super H-magic and super (a; d)-H-antimagic for some d.