Geodesic
Signed degree sets in signed graphs
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 843-848

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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.
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.
Classification : 05C07, 05C20, 05C22
Keywords: signed graphs 
Pirzada, S.; Naikoo, T. A.; Dar, F. A. Signed degree sets in signed graphs. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 843-848. http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a4/
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     title = {Signed degree sets in signed graphs},
     journal = {Czechoslovak Mathematical Journal},
     pages = {843--848},
     year = {2007},
     volume = {57},
     number = {3},
     mrnumber = {2356284},
     zbl = {1174.05059},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a4/}
}
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