Aisha AsgharSP18-RMT-020LHR TP 6546Dr. Muhammad Hussain2026-03-122020https://repository.cuilahore.edu.pk/handle/123456789/2755Graph labeling plays a very significant function in implementations in graph theory such as network, correspondence naming, X-ray, circuit modeling, crystallography, radar, rocket navigation, astronomy and data base administration. A labeling is bijective mapping, in which vertices or edges are assigned to natural numbers. If the weights of all vertices are identical, then these labels are considered magic labeling. In 2000, Baca et al.[5] presented the idea of total antimagic labelling of (a, d)-vertex. A labeling in which both vertices and edges compose of domain collection is called total labeling. If we assign the smallest number to vertices and then to edges, a labeling is called super (a, d)-vertex total antimagic labelling. Hussain et. Al. [17,18] formulated (a,d)-vertex antimagic total labeling on Harary graghs, however, many cases are still open. This dissertation learning about the configuration of new results of (a,d)-vertex anti-supermagic total (VAST) labeling of Harary graphs. Also we construct same new esults of super (a,d)-vertex magic total(SVT) labeling on Harary graphs.enDr. Muhammad Hussainsp18Department of MathematicsMathematicsvertex anti-supermagic total (VASTThesis