%0 Journal Article
%T Diameter Two Graphs of Minimum Order with Given Degree Set
%J Mathematics Interdisciplinary Research
%I University of Kashan
%Z 2538-3639
%A Abrishami, Gholamreza
%A Rahbarnia, Freydoon
%A Rezaee, Irandokht
%D 2016
%\ 07/01/2016
%V 1
%N 2
%P 317-323
%! Diameter Two Graphs of Minimum Order with Given Degree Set
%K Degree set
%K self-centered graph
%K radius
%K diameter
%R 10.22052/mir.2016.34107
%X 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.
%U https://mir.kashanu.ac.ir/article_34107_f8c714c2b1ea6bcadfdfe4ef88683da2.pdf