Linear programming formulation for some generalized domination parameters

Abstract

An enormous number of domination parameters have been defined and studied, because of their applications in various fields of science and engineering. From it, we have selected some variation of domination parameters and its generalized form for the study. We have presented a linear programming formulation with linear number of constraints for the selected parameters. MATLAB algorithmic code has been generated to find a minimum dominating set/function and the domination number of the selected parameters. The domination number and its computational time of five generalized domination parameters, [Formula: see text]-domination, [Formula: see text]-domination, efficient [Formula: see text]-domination, factor domination and [Formula: see text]-domination, have been studied under grid graphs and randomly generated graphs. The computational time for efficient [Formula: see text]-domination and [Formula: see text]-domination numbers is less than [Formula: see text] s, which shows the effectiveness of the formulation.