TY - JOUR
ID - 34107
TI - Diameter Two Graphs of Minimum Order with Given Degree Set
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Abrishami, Gholamreza
AU - Rahbarnia, Freydoon
AU - Rezaee, Irandokht
AD - Department of Applied Mathematics,
Ferdowsi University of Mashhad,
P. O. Box 1159, Mashhad 91775, Iran
Y1 - 2016
PY - 2016
VL - 1
IS - 2
SP - 317
EP - 323
KW - Degree set
KW - self-centered graph
KW - radius
KW - diameter
DO - 10.22052/mir.2016.34107
N2 - 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.
UR - https://mir.kashanu.ac.ir/article_34107.html
L1 - https://mir.kashanu.ac.ir/article_34107_f8c714c2b1ea6bcadfdfe4ef88683da2.pdf
ER -