Category Archives: Math

Sage 4.7.1 in Ubuntu Oneiric

Since I am starting a clean install of the new Ubuntu, I proceeded to reinstall Sage. After the usual steps, and running sage, I got an error message, which I had not seen before, starting with: ————————————————————————— ImportError Traceback (most … Continue reading

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Graph theory in Sage

Even though there are already fine guides in the web to start using the Sage software for graph theory, such as this, a video, and this, I wanted to write a simple one for my students. We have been studying … Continue reading

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Is the Franklin graph a Cayley graph?

The Franklin graph is one of the four vertex-transitive cubic graphs on 12 vertices. From its drawing it is easy to see it is actually vertex-transitive, but I wanted to check whether it is a Cayley graph. I would use … Continue reading

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Graphs 003: Graph families

Complete graphs The complete graph , is the graph with vertices, such that every pair of vertices is adjacent. Paths The path , is the graph with and . Cycles The cycle , is the graph with and . Complete … Continue reading

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Graphs 002: Connectedness, diameter and girth

Connectedness Let be a graph. A path in is a sequence of distinct vertices of , such that for . In this case, we say that the path is a -path and that it has length . We say that … Continue reading

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Graphs 001

Definitions and examples A (finite, simple) graph is an ordered pair of two finite sets, where is a set of -element subsets of . The vertices of are the elements of , and the edges of are the elements of … Continue reading

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