Algorithmic Techniques for the Generation and Analysis of Strongly Regular Graphs and other Combinatorial Configurations

In this paper we examine computing techniques applicable to the construction and analysis of combinatorial configurations. These techniques are first described for arbitrary configurations and then elaborated for a particular example. The generation procedures which are reviewed are backtracking and hill-climbing. In order to analyse a configuration it is often necessary to employ heuristic algorithms since the properties to be determined constitute an NP-complete problem. Various heuristic strategies are discussed for such analyses. The example consists of the family of strongly regular graphs with parameter sets (25, 12, 5, 6) and (26, 10, 3, 4). For these strongly regular graphs we present some original generation techniques as well as new results on properties of these graphs.

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