A CHARACTERIZATION OF (Cn;K1;n)-SUPERMAGIC OF TREES CORONA PATHS AND TREES JOIN A TRIVIAL GRAPH

• Main Author: Fadhilah Ashari, Yeva
• Format: Theses
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/32165
• Institution: Institut Teknologi Bandung

Let H1 and H2 be two simple connected graphs. A graph G = (V (G);E(G)) admits an (H1;H2)-covering, where H1 and H2 are two subgraphs of G, if every edge in E(G) belongs to at least one subgraph of G isomorphic to H1 or H2. The graph G is called an (H1;H2)-magic, if there exists a bijective function f : V (G) [ E(G) ! f1; 2; :::jV (G)j + jE(G)jg and two positive integers k1 and k2 such that w(H 0 ) = X v2V (H0 ) f(v) + X e2E(H0 ) f(e) = k1 for every subgraphs H0 of G isomorphic to H1 and w(H 00 ) = X v2V (H00 ) f(v) + X e2E(H00 ) f(e) = k2: for every subgraphs H0 of G isomorphic to H1. Furthermore, G is called (H1;H2)- supermagic, if f(V (G)) ! f1; 2; :::; jV (G)jg. A graph G corona graph H, denoted by GH is a graph which is obtained from G and jV (G)j copies of H, namely H1;H2; :::;HjV (G)j, and joined every vi 2 V (G) to all vertices in V (Hi) for i 2 f1; 2; :::; jV (G)jg. In this thesis, we give a necessary condition of G being a (Cn;K1;n)-magic, and a characterization of (Cn;K1;n)- supermagic of trees corona paths T Pm for any n 3 and m 2. Besides that, we study a characterization of (Cn;K1;n)-supermagic of trees join a trivial graph T + K1 for n 2 f3; 4g. The graph G join H denoted by G + H is a graph that is obtained from G union H and joined every vertex in G to all vertices in H.