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Cyclic bilinear forms of enumerated graphs. (English. Russian original) Zbl 0813.05066
Russ. Acad. Sci., Dokl., Math 48, No. 1, 10-13 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 331, No. 1, 11-13 (1993).
Summary: We consider graphs with enumerated vertices (\(\Pi\)-graphs). In our papers [Russ. Math. Surv. 47, No. 4, 206-2097 (1992); translation from Usp. Mat. Nauk 47, No. 4(286), 189-190 (1992; Zbl 0791.05097)] and [Russ. Acad. Sci., Dokl., Math. 46, No. 1, 36-42 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 325, No. 2, 221-226 (1992; Zbl 0795.05077)] each \(\Pi\)-graph is put into correspondence with a bilinear form whose variables correspond to the vertices. This mapping has the following remarkable property. If a \(\Pi\)-graph is absolutely separated (i.e. no four of its vertices induce the simple chain \(P_ 4\)), the corresponding bilinear form is identically zero. In this note we construct another mapping with the same property.

05C99 Graph theory
15A63 Quadratic and bilinear forms, inner products
05C30 Enumeration in graph theory