engleski

New strongly regular graphs from orthogonal groups O+(6,2) and O−(6,2)

We prove the existence of strongly regular graphs with parameters (216, 40, 4, 8) and (540, 187, 58, 68). We also construct a strongly regular graph with parameters (540, 224, 88, 96) that was previously unknown. Further, we construct all distance-regular graphs with at most 600 vertices, admitting a transitive action of the orthogonal group O+(6, 2) or O- (6, 2). Furthermore, we show that under certain conditions an orbit matrix M of a strongly regular graph Gamma can be used to define a new strongly regular graph (Gamma) over tilde where the vertices of the graph (Gamma) over tilde correspond to the orbits of Gamma (the rows of M). We show that some of the obtained strongly regular graphs are related to each other in a way that one can be constructed from an orbit matrix of the other.

Strongly regular graph ; Distance-regular graph ; Orthogonal group ; Orbit matrix

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