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Euler Circuits and Euler Paths. In this video I discuss the ideas of: paths, multigraphs, euler paths, euler circuits, the necessary and sufficient condition for a graph to have an euler path or euler circuit, along with an applied problem.

A four-by-four table of particles. Columns are three generations of matter (fermions) and one of forces (bosons). In the first three columns, two rows contain quarks and two leptons. The top two rows' columns contain up (u) and down (d) quarks, charm (c) and strange (s) quarks, top (t) and bottom (b) quarks, and photon (γ) and gluon (g), respectively. The bottom two rows' columns contain electron neutrino (ν sub e) and electron (e), muon neutrino (ν sub μ) and muon (μ), and tau neutrino (ν sub τ