Edge-Magic Total Labeling on Vertex Amalgamation Graphs of a Star Graph with a Path Graph - Selfa Suwandi; Nurdin Nurdin; Muh. Nur (Syntax Corporation Indonesia, 2024)
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 .