University of KashanMathematics Interdisciplinary Research2538-36391220160701Diameter Two Graphs of Minimum Order with Given Degree Set3173233410710.22052/mir.2016.34107ENGholamreza AbrishamiDepartment of Applied Mathematics,
Ferdowsi University of Mashhad,
P. O. Box 1159, Mashhad 91775, IranFreydoon RahbarniaDepartment of Applied Mathematics,
Ferdowsi University of Mashhad,
P. O. Box 1159, Mashhad 91775, IranIrandokht RezaeeDepartment of Applied Mathematics,
Ferdowsi University of Mashhad,
P. O. Box 1159, Mashhad 91775, IranJournal Article20160502The 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.https://mir.kashanu.ac.ir/article_34107_f8c714c2b1ea6bcadfdfe4ef88683da2.pdf