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

Selfa Suwandi (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Hasanuddin)
Nurdin Nurdin (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Hasanuddin)
Muh. Nur (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Hasanuddin)

Journal of Social Science
Vol. 5 No. 4 (2024): Journal of Social Science

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 .