Pelabelan Titik Bimagic Terbalik Super pada Path Related Graphs

Abstract

A graph  is a connected, undirected, and simple graph where  is a set of vertices and  is a set of edges. Graph  with  vertices and  edges is said to admit a reverse vertex bimagic labeling if there exists a bijection  such that for each ,  for two distinct  and . Then, reverse vertex bimagic labeling is called super if label of edges are . A graph  that admits reverse super vertex bimagic labeling is called reverse super vertex bimagic graph.  The concept of reverse super vertex bimagic labeling in graph labeling arises from the existence of graphs that admit a reverse super vertex bimagic labeling but do not admit a reverse super vertex magic labeling. In addition, this concept aims to extend the range of magic constants, which were initially restricted to positive values, to include non-negative values. In this research, we investigated reverse super vertex bimagic labeling of path related graph, there are path graph , brush graph  and centipede tree graph .The method used is an explicit construction of a bijective labeling function .  The results show that path graph, brush graph  and centipede tree graph  are reverse super vertex bimagic graphs with the bimagic sums of each being , for path graph, , for brush graph, and  for centipede tree graph.