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Representations of symmetric graphs

Theory of vertex-transitive maps, especially certain structural properties of automorphism groups of graphs, are important aspects in graph representations of highly symmetric combinatorial structures. In this context, covering graph algorithms are a powerful tool in classifications as well as in obtaining representations of cover graphs using the knowledge of representations of base graphs [15, 16]. The objective of this part is to establish a computer library in Magma containing certain useful graph covering routines that could be further used in various contexts. Under this theme aspects of edge-transitivity and s-arc-transitivity), will be studied. Similarly, a special attention will be given to description of cubic and quartic graphs admitting arc-transitive group actions and classification of special structures from which interesting (partial) geometries arise (association schemes, strongly regular graphs, cages).

Ivolved: Marušič, Škoviera, Conder, Klin