The Four-Distance Domination Number in the Ladder and Star Graphs Amalgamation Result and Applications

Abstract

The study purpose is to determine the four-distance domination number in the amalgamation operation graph, namely the vertex amalgamation result graph of ladder graph Amal(L_m,v,n) with m≥2 and n≥2 and the vertex amalgamation result graph of a star graph with its name Amal(S_m,v,n) with m≥2 and n>2. In addition, the application use the Four-distance domination number on Jember Regency Covid-19 taskforce post-placement. The Importanceof this research, namely the optimal distribution of the Covid-19 task force post. It is not just doing mask surgeries every day on the streets. The optimal referred to can be in the form of integrated handlers in each sub-district or points that are considered to need fast handling so that coordination between posts can respond and immediately identify cases of transmission and potential infections due to interactions with patients who are already positive. The methods used in this research are pattern recognition and axiomatic deductive methods. The results of this study include:γ_4 (Amal(S_m,v,n))=1; for m≥2 and n≥2, γ_4 (Amal(L_m,v,n))={■(1; for 2≤m≤4 @⌊m/8⌋n+1 for m≡0,1,2,3,4 (mod 8)@⌈m/8⌉n; for others m ) ┤ and based on the Indonesia Country, Jember Regency Map, 2 Covid 19 task-force posts are needed to be placed in Balung and Kalisat sub-districts using the Four-distance domination number application.

Connected metric dimension of the class of ladder graphs

“…Interference can be prevented with the proper channel assignment. To arrive at a solution, Hale [27][28][29][30] conceptualized the problem as a graph (vertex) coloring model, which we now refer to as the 𝐿(2,1) coloring. Consider about the different transmitters and stations that are out there.…”