Randunu, M.W.S.Athapattu, A.M.C.U.M.2026-03-122026-03-122022-10-28Proceedings of the Postgraduate Institute of Science Research Congress (RESCON) -2022, University of Peradeniya, P 100978-955-8787-09-0https://ir.lib.pdn.ac.lk/handle/20.500.14444/7630Graph labeling has been an exciting area of research in graph theory. Most graph labeling origins can be traced back to the mid-1960s. Over the last 60 years, more than 100 graph-labelling techniques have been studied. E-super vertex magic labeling is a type of modern concept when compared with other popular labeling patterns such as graceful labeling, harmonious labeling, lucky labeling, anti-magic labeling, etc. It is one of the most challenging and interesting labeling techniques with various applications. For a finite simple graph G, the set of vertices and edges are denoted by V(G) and E(G), respectively. If G is a simple undirected graph with p vertices and q edges, then vertex magic total labeling is a bijective map f from V(G) ∪ E(G) onto the set { 1, 2, . . . , p + q, } with the property that, for every vertex u in V(G), f(u)+ ∑ V∈N(u)f (uv) = k, where k is a constant and set N(u) denotes the vertices adjacent to the vertex u. The labeling is called E-super vertex magic if f(E(G)) = {1, 2, ... , q}. A graph G is called E-super vertex magic if it admits an E-super vertex magic labeling. Intending to answer the open problem, every tree is E- super vertex magic to some extent; we focus on the E-super vertex magic labeling for the caterpillar graph. In this study, we can prove that E-super vertex magic labeling does not exist for the star graphs Sₙ with n ≥ 4. Consequently, we proved that the caterpillar graph, which has a star graph as a subgraph, is not an E- super vertex graph for order; n ≥ 7.en-USCaterpillar graphE-super vertex magic labelingStar graphArticle