Abstract

MARRERO, Osvaldo  and  PASLES, PaulC.. A combinatorial problem on a directed graph. Rev. Mat [online]. 2016, vol.23, n.2, pp.409-420. ISSN 1409-2433.

We consider two options for a particle's entire journey through a certain directed graph. Both options involve a random assignment to the journey route to be followed. We are interested in the option that offers, on average, the shortest route. Therefore, we determine the average journey length for each of the two options. As part of our analysis, we prove some combinatorial identities that appear to be new. Some suggestions for further work are given.

Keywords : directed graphs; games on graphs; combinatorial identities; combinatorial probability.

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