DIMENSI PARTISI GRAF HASIL KALI 2-KUAT DAN PROGRAM PENCARI PARTISI PEMBEDA BEBERAPA KELAS GRAF
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...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/55335 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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