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Signed degree sets in signed graphs

S. Pirzada·T. A. Naikoo·F. A. Dar
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Abstract

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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S. Pirzada, T. A. Naikoo, F. A. Dar. 2006-09-05. Signed degree sets in signed graphs. https://arxiv.org/abs/math/0609121

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