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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.

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