01191251

j

01191251 Vesnin, A.Yu. Dobrynin, A.A. The Yamada polynomial for graphs, embedded knot-wise into three-dimensional space. Vychisl. Sist. 155, 37-86 (1996). 1996 Rossijskaya Akademiya Nauk, Institut Matematiki, Novosibirsk RU The authors study polynomial invariants for knotted graphs in 3-space. For a plane diagram of any graph in ${\Bbb R}^3$ they associate a so-called Yamada polynomial whose expression is too long to be given here. The authors describe how this polynomial behaves under Reidemeister moves. The Yamada polynomial for particular graphs (those which are obtained from toric knots by adding an arc) is explicitly calculated. An algorithm and a computer program for computing the Yamada polynomial for graphs are given, and the values of the Yamada polynomial for certain graphs are tabulated. The results of the papers may have applications to biology and chemistry. L.Potyagailo (Villeneuve d'Ascq)