Document Type : Original Scientific Paper

**Authors**

Department of Applied Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran

**Abstract**

The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for a given set of natural numbers greater than one, we determine the minimum order of a 2-self-centered graph with that degree set.

**Keywords**

**Main Subjects**

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