International conference
Combinatorial Methods in Physics and Knot Theory

Energies of knots are functionals on the space of smooth or piecewise smooth knots, this depends on the type of energy. We consider the best-known energies of knots: Mobius energy, energy of osculating circles and some other energy functionals, and also we present a new Mm-energy of a knot. The most important properties of the energies are continuity, positivity, and the property that the energy tends to infinity while the knot tends to some knot with self-crossings. This properties of energies give another approach to the problem of identification the knot type for some given knot based on variational principles. The described approach can be generalized to the case of graphs for some special types of energies. We will study Mm-energy of graphs more detailed.