Abrishami, G., Rahbarnia, F., Rezaee, I. (2016). Diameter Two Graphs of Minimum Order with Given Degree Set. Mathematics Interdisciplinary Research, 1(2), 319-325. doi: 10.22052/mir.2016.34107

Gholamreza Abrishami; Freydoon Rahbarnia; Irandokht Rezaee. "Diameter Two Graphs of Minimum Order with Given Degree Set". Mathematics Interdisciplinary Research, 1, 2, 2016, 319-325. doi: 10.22052/mir.2016.34107

Abrishami, G., Rahbarnia, F., Rezaee, I. (2016). 'Diameter Two Graphs of Minimum Order with Given Degree Set', Mathematics Interdisciplinary Research, 1(2), pp. 319-325. doi: 10.22052/mir.2016.34107

Abrishami, G., Rahbarnia, F., Rezaee, I. Diameter Two Graphs of Minimum Order with Given Degree Set. Mathematics Interdisciplinary Research, 2016; 1(2): 319-325. doi: 10.22052/mir.2016.34107

Diameter Two Graphs of Minimum Order with Given Degree Set

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.