Edge-Magic Total Labeling on Vertex Amalgamation Graphs of a Star Graph with a Path Graph

Abstract

One of the topic graph theories is graph labeling. Let  be a finite simple connected graph, a bijection  from  to  where  and  is called an edge-magic total labeling of  if there exists a contant (called the magic sum of ) such that  for any edge  of . The super edge-magic total labeling on a graph  is the edge-magic total labeling which maps  into the set . Let  be a connected graph with a fixed vertex . The vertex amalgamation of graph  onto a fixed vertex  called terminal denoted by  is a graph formed by taking all elements (vertices and edges) in  with . In this study, we will show that vertex amalgamation graphs of a star graph with a path graph are edge-magic total and super edge-magic total labeling, with constructed vertex labelings and edge labelings to obtain intervals of the magic sums .