Signed degree sets in signed graphs

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The set D of distinct signed degrees of the vertices in a signed graph G is called its signed degree set. In this paper, we prove that every non-empty set of positive (negative) integers is the signed degree set of some connected signed graph and determine the smallest possible order for such a signed graph. We also prove that every non-empty set of integers is the signed degree set of some connected signed graph.

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Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/116379

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0609121
 http://arxiv.org/abs/math/0609121

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arXiv