The diversity of birds in Koonthankulam pond, located in Koonthankulam village (8.495N, 77.755E), Tirunelveli district, southern Tamil Nadu, was studied. A total of 90 species belonging to 21 orders, 42 families, and 73 genera were recorded. The study recorded seasonal migrants such as Black Ibis, Oriental White Ibis, Bar-headed Goose & Spoonbill and indigenous species including the Pond Heron, Cattle Egret, White-breasted Kingfisher, Red-wattled Lapwing, Rose-ringed Parakeet, Purple-rumped Sunbird, Hoopoe, and Indian Robin. The primary data were analyzed by principal component analysis, cluster, and analysis of variance. Analysis of variance showed that the Menhinick index is statistically significant P <0.05.  A structural equation model was applied to analyze the physico-chemical parameters of water samples collected from the sampling site. Analysis of experimental data through the structural equation model indicates temperature and dissolved oxygen may indirectly affect bird diversity.

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.

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.

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.