WHEEL-SUPERMAGIC LABELINGS FOR A WHEEL CORONA MULTILEVEL-k WITH A CYCLE

• Main Author: HOGLA TATI MARBUN ( NIM :10108102); Pembimbing : Prof Dr. M. Salman A. N
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/15953
• Institution: Institut Teknologi Bandung

Graph G corona graph H, denoted by G H, is the graph that obtained from one copy of G and |V(G) | copies of H, namely H1, H2, ..., H|V(G)| , and joining the and joining the point-i vertex of G with an edge to every vertex in the G dan |V(G) | copy of H. Let k be a positive integer. A graph G1 corona multilevel-k with a graph G2, denoted by G1 corona k G2, a graph that defined by (G1 corona k G2) korona G2 for k > 2 and graf G1 corona G2 for k =1. Graf G =(V,E) is said to be H-magic if every edge of G belongs to at least one <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> subgraph isomorphic to H and there is a total labeling f :V(G)Bigcup E(G)->(1,2,..., |V(G) | + | E(G)|) such that for each subgraph H' = (V ',E') of G isomorphic to H, the sum of all vertex labels in V' plus the sum of all edge labels <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> in E' is a constant. Additionally, G is said to be H-supermagic if f (V(G)) =(1,2,3,...,|V(G) |). We prove that a wheel Wn corona multilevel-k with a cycle Cn is Wn-supermagic.