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