Signed degree sets in signed bipartite graphs

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A signed bipartite graph G(U, V) is a bipartite graph in which each edge is assigned a positive or a negative sign. The signed degree of a vertex x in G(U, V) is the number of positive edges incident with x less the number of negative edges incident with x. The set S of distinct signed degrees of the vertices of G(U, V) is called its signed degree set. In this paper, we prove that every set of integers is the signed degree set of some connected signed bipartite graph. \medskip \medskip

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Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/116380

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0609122
 http://arxiv.org/abs/math/0609122

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arXiv