Pelabelan Jarak Tak Teratur Titik Pada Graf Persahabatan Lengkap Diperumum

Abstract

Graph labeling is the labeling of graph elements such as vertex, edge and both. distance vertex irregular labeling is a type of labeling resulting from the development of distance magic labeling and (a, b)-distance anti-magic labeling.  Let   , be a simple graph.  The distance vertex irregular labeling of  is a vertex labeling so that the weight of each vertex    is different. The weight of    is calculated based on the sum of vertices  label  in  the set of neighboring vertex , namely  Distance vertex  irregularity  strength of   , denoted as d , is the smallest value of the largest label  so that  has a distance vertex irregular labeling.  This study aims to construct a generalized complete friendship graph , determine the labeling function, determine the distance vertex irregularity strength then formulate and prove the theorem resulting from the labeling. The object of this research is to label each vertex on a generalized complete friendship graph. This research method is a literature study obtained through various sources. Based on the research results, it is known that the graph  has distance vertex irregular labeling. For an integer m and n, , the  labeling  function of   is  and . Distance vertex  irregularity  strength of generalized complete friendship graph is   .