DIMENSI PARTISI GRAF HASIL KALI 2-KUAT DAN PROGRAM PENCARI PARTISI PEMBEDA BEBERAPA KELAS GRAF

• Main Author: Aliya Fiddien, Ilma
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/55335
• Institution: Institut Teknologi Bandung

Let ???? be a non-trivial graph with the vertices set ????¹????º and the edges set ????¹????º. For each ???? 2 ????¹????º and ???? ????¹????º, distance between ???? and ????, ????¹????? ????º is the shortest distance between ???? and a vertex in ????. The representation of ???? with respect to an ordered partition? = f????1? ????2? ???? ???????? g is a ????-vector ???? ¹????j?º = ¹????¹????? ????1º? ????¹????? ????2º? ???? ????¹????? ???????? ºº. ? is resolving partition for ???? if all representation of vertices of ???? with respect to ? is unique. Dimension partition of ????, denoted by ????????¹????º, is the smallest cardinality of resolving partitions for ????. In this research, for ???? and ???? any graphs with minimum diameter ????, we define a ????-strong product graph, ???? ???? ????, a generalization of strong product graph. Through pattern-finding, we formulate the diameter of 2-strong product graphs of paths, cycles, and complete bipartite graphs. We then determine boundaries for partition dimension of 2-strong product graphs by utilizing the order and diameter of the original graphs. We involved 2???????? power graph to help find resolving partition of ???? 2 ????. In the last section, we show a resolving partition finder program for few graph classes which written in Python.