Binary nullity, Euler circuits and interlace polynomials
نویسندگان
چکیده
منابع مشابه
Binary nullity, Euler circuits and interlace polynomials
A theorem of Cohn and Lempel [J. Combin. Theory Ser. A 13 (1972), 83-89] gives an equality involving the number of directed circuits in a circuit partition of a 2-in, 2-out digraph and the GF (2)-nullity of an associated matrix. This equality is essentially equivalent to the relationship between directed circuit partitions of 2-in, 2-out digraphs and vertexnullity interlace polynomials of circl...
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The interlace polynomials extend in a natural way to invariants of graphs with vertex-weights, and these weighted interlace polynomials have several novel properties. One novel property is a version of the fundamental three-term formula q(G) = q(G − a) + q(G − b) + ((x − 1) − 1)q(G − a − b) that lacks the last term; consequently the use of vertex-weights allows for interlace polynomial calculat...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2011
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.02.004