A Study of Independent Domination in Block Designs: Focus On PBIB-Designs

Partially Balanced Incomplete Block (PBIB) designs are the primary subject of this investigation of independent dominance in block designs. In the combinatorial structure of PBIB-designs, where treatments and blocks are depicted as vertices and edges, respectively, the graph-theoretic parameter known as independent dominance is applied. Within the framework of PBIB-designs defined by different association schemes, the study delves into the theoretical foundations, computation, and consequences of independent domination. Finding autonomous dominating sets that effectively represent all treatments while minimizing redundancy is the goal of the study, which offers a paradigm for doing so by examining the links between blocks and treatments. Experiment design optimization using independent dominating parameters is demonstrated in case studies of 2-associate and 3-associate PBIB-designs. This study sheds light on the structural features of PBIB-designs by demonstrating the interaction between graph theory and combinatorial design theory. In situations where resources are limited, it highlights the value of independent dominance as a method for assessing and improving block designs’ efficiency. Our current understanding of block designs and how to optimize them for use in experimental planning, data analysis, and resource allocation is enhanced by these findings.