INDEPENDENT [1,2]-SET IN SEVERAL COMB EDGE GRAPH

• Main Author: Adriansyah Ruswandi, Muhammad
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/85824
• Institution: Institut Teknologi Bandung

Let ???? be a simple graph with vertex and edge sets ????(????) and ????(????) respectively. Suppose ?????????(????). The set ???? is called a independent [1,2]-set of ???? if any two distinct vertices in ???? are not adjacent, and every vertex ?????????(????)????? is adjacent to exactly one or two vertices in ????. The minimum cardinality of all independent [1,2]-set of ???? is called the [1,2]-independent number of ????.For two connected graphs ???? and H, the comb edge graph of ???? and ???? over an edge ?????????(????) denoted by ????????????? is the graph obtained from|????(????)| copies of ???? and one copy of ????, by identifying the ????-th copy of ???? at edge ???? with the ????-th edge of ????. In this final project, several simple graphs that have independent [1,2]-sets are presented. Furthermore, for ????,the complete graph ???????? and the complete bipartite graph ????????,???? such that ????????????????? and ?????????????????,???? have independent [1,2]-sets are showed. Finally, the exact values of the [1,2]-independent number for ????, ????????, and ????????,????, such that ????????????????? and ?????????????????,???? have 1,2-independent sets, are determined.