Determination of the Restrained Domination Number on Vertex Amalgamation and Edge Amalgamation of the Path Graph With the Same Order

Abstract

Graph theory is a mathematics section that studies discrete objects. One of the concepts studied in graph theory is the restrained dominating set which aims to find the restrained dominating number. This research was conducted by examining the graph operation result of the vertex and edges amalgamation of the path graph in the same order. The method used in this research is the deductive method by using existing theorems to produce new theorems that will be proven deductively true. This research aimed to determine the restrained dominating number in vertex and edges amalgamation of the path graph in the same order. The results obtained from this study are in the form of the theorem about the restrained dominating number of vertex and edges amalgamation of the path graph in the same order, namely: for , ⌋, and for , ⌋.

Himpunan Dominasi Terkendali Graf Hasil Operasi Amalgamasi Titik Dan Sisi Pada Graf Siklus Berorde Sama

“…Sedangkan "On equality in an upper bound for the restrained and total domination numbers of a graph" [6] dan "Restrained Domination in Unicyclic Graphs" [7] masing -masing memperoleh hasil batas atas dan batas bawah bilangan dominasi terkendali dari suatu graf. Selain itu, penelitian tentang himpunan dominasi terkendali yang melibatkan operasi graf dari beberapa graf khusus juga telah banyak dikaji, diantaranya "Restrained Domination in Graphs Under Some Binary Operations" [8], "The Product of the Restrained Domination Numbers of A Graph and Its Complement" [9], "Secure Restrained Domination in the Join and Corona of Graphs" [10], "Penentuan Bilangan Dominasi Terkendali pada ' ⨀' dan ( ⨀( " [11], dan "Determination of the Restrained Domination Number on Vertex Amalgamation and Edge Amalgamation of the Path Graph With the Same Order" [12].…”