PELABELAN SISI TITIK-ANTI AJAIB PADA t KOPI GRAF BIPARTIT

• Main Author: SUKMANA PRAJA (NIM: 20110005); Pembimbing : Prof. Dr. M. Salman A.N., ALFAN
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/14794
• Institution: Institut Teknologi Bandung

LetG = (V,E) be a simple graph. An injective function ro : E -> (1,2,3, 3,..., (E) is called a vertex-antimagic edge labeling if every two distinct vertices have different weight. The weight of a vertex u in V under function W(u)= ro (uv). Additionally ro is called an (a,d)-vertex-antimagic edge labeling if there exist two positive integer a and d such that W(V ) = (a,a + d,a+2d,...a + ((V)-1)d). A bipartite graph is a graph whose vertices can be divided into two disjoint sets A and B such that every edge connects a vertex in A to one in B. A complete bipartite graph Kn,m is a bipartite graph such that (A)= n, (B) = m and for any two vertices u in A and v in B, uv is an edge in Kn,m: A matching M < E is a collection of edges such that every vertex v in V is incident to at most one edge of M. A matching is perfect if every vertex v in V is incident to exactly one edge of M. In this thesis, we consider a complete bipartite graph Kn,m minus a perfect matching for n > 4, denoted by Gn. For an odd t and an even n that more than t, we prove that tGn minus perfect matching has a vertex antimagic edge labeling. Then, for an integer t and an even n that more than 3, tK,n has a vertex 2,n)-antimagic edge labeling. Moreover, we also <br /> <br /> <br /> <br /> <br /> <br /> <br /> prove a complete bipartite graph Kn,m minus a maximum matching has a vertex antimagic edge labeling for any positive integer n and m.