MULTIPLE DIAMOND GRAPH LABELINGS

• Main Author: Arif Susilo, Alfiatri
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/71878
• Institution: Institut Teknologi Bandung

Let G = (V (G),E(G)) be afinite,undirected,andsimplegraph.Thisstudyuses diamond graphs.Foranaturalnumber n with n ? 2, adiamondgraphthathas 2n vertices and 5n ? 5 edgesisdenotedby Brn. Observedseverallabelsonadia- mond graph,suchasanedge-magicvertex-labeling,avertex (a, d)-edgeantimagic labeling,avertex-magicedge-labeling,anedge (a, d)-vertexantimagiclabeling,a vertexmagictotallabeling,anedgemagictotallabeling,amagic-C3 total-labeling, and atotal (a, d)-C3-antimagicgraphlabeling.Weobtainsomeresultsasfollows. A graph Br2 has anedge (a, d)-vertexantimagiclabeling,avertexmagictotallabe- ling,anedgemagictotallabeling,amagic-C3 total-labeling,andatotal (a, d)-C3- antimagicgraphlabeling,buthasnoanedge-magicvertex-labeling,avertex-magic edge-labeling,andanedge (a, d)-vertexantimagiclabeling.For n ? 3, agraph Brn has noedge-magicvertex-labelingandvertex (a, d)-edgeantimagiclabeling. It isalsoshownthatthegraph Brn for n ?= 20 has avertex-magicedge-labeling if andonlyif n = 4 or n = 5. Thengiventhenecessaryconditionthatagraph Brn for any n ? 3 has anedge (a, d)-vertexantimagiclabeling.Besidesthat, given amagicconstantvalueofagraph Brn for any n ? 3 whichhasavertex- magictotal-labeling,anedge-magictotal-labeling,amagic-C3 total-labeling,or an (a, d)-C3-anti magictotal-labeling.