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Speaker: Daniela Ferrero, Texas State University-San Marcos

Title: Topological properties of path graphs

Abstract: Among the many graph-valued functions or graph operators, the line graph is undoubtedly the most important one, due to their usefulness in a broad range of problems from different disciplines. However, in order to optimize their use in certain applications, many variations of this operator have been recently introduced. This is the case of path graphs, whose iterated application seems to be a very promising alternative to iterated line graphs as interconnection network models. We will survey some results regarding topological properties of iterated path graphs, such us connectivity, cycles, diameter and distances, and present a wide range of open problems not only in relation to their topology, but also regarding routing problems, symmetry, graph dynamics, algebraic properties, and finally their possible applications in other fields.

Speaker's email: dferrero@txstate.edu

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