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Using two backtrack algorithms based on different techniques, designed and implemented independently, we were able to determine up to isomorphism all strongly regular graphs with parameters v = 45, k = 12, λ = µ = 3. It turns out that there are 78 such graphs, having automorphism groups with sizes ranging from 1 to 51840.
By means of an exhaustive computer search we have proved that the strongly regular graphs with parameters (v, k, λ, µ) are unique upto isomorphism. Each of these graphs occurs as an induced subgraph in the strongly regular McLaughlin graph. We have used an orderly backtracking algorithm with look-ahead and look-back strategies, applying constraints based on… (More)
During the past few years we have obtained several new computer classification results on association schemes and in particular distance regular and strongly regular graphs. Central to our success is the use of two algebraic constraints based on properties of the minimal idempotents E i of these association schemes : the fact that they are positive… (More)
The McLaughlin graph  is a strongly regular graph on 275 vertices which contains several interesting strongly regular graphs as a subgraph. Several of those strongly regular subgraphs are known to be unique for their parameter set [1, 2, 3, 4]. Only for four parameter sets the uniqueness was not yet settled. Using an exhaustive orderly algorithm in… (More)
SUMMARY Splay trees are widely considered as the classic examples of self-adjusting binary search trees and are part of probably every course on data structures and algorithms. Already in the first seminal paper on splay trees  alternative operations were introduced, among which semi-splaying. On the one hand the analysis of semi-splaying gives a smaller… (More)
We are interested in the exhaustive generation (up to isomorphism) by computer of all association schemes  (strongly regular graphs, distance regular graphs, ...) with a given parameter set. The generation algorithms require a recursive traversal of a tree-like search space. We use various pruning methods and heuristics to limit the size of the search… (More)