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A restrained dominating set [Formula: see text] is said to be a strong restrained dominating set of G if every vertex [Formula: see text] is adjacent to a vertex [Formula: see text] and [Formula: see text]. The minimum cardinality of a strong restrained dominating set of G is said to be the strong restrained domination number of [Formula: see text] and it is denoted by [Formula: see text]. We characterize all the trees with [Formula: see text]. We show that if [Formula: see text] is a tree of order [Formula: see text], then [Formula: see text] and characterize the extremal trees by achieving this lower bound. Simulation was carried out for the strong restrained domination number of Cartesian, strong and lexicographic product under four different network topologies and it was noted that [Formula: see text] under these four network topologies. Furthermore, the strong restrained domination number of [Formula: see text] and [Formula: see text] for any [Formula: see text] and [Formula: see text] for any [Formula: see text] is determined.

Domination is an emerging field in graph theory and many domination parameters were introduced in the meanwhile for different real time situations. Minimum domination number of a graph can be identified by converting the problem into linear programming problem (LPP). In this paper, LPP formulation for strong domination number, restrained domination number and strong restrained domination were developed. MATLAB program was coded to find the values of these parameters. The chain relations among these parameters are tried in four different types of network topologies. Simulation for these four parameters under four network topologies were conducted and it was noticed that in three network types, [Formula: see text] whereas, in the other one, [Formula: see text]. An improved upper bound for restrained domination number was approximated by using the probabilistic method.