Applicable Analysis and Discrete Mathematics 2021 Volume 15, Issue 2, Pages: 393-412
https://doi.org/10.2298/AADM171211019K
Full text (
405 KB)
Cited by
The Roman domination number of some special classes of graphs - convex polytopes
Kartelj Aleksandar 
(University of Belgrade, Faculty of Mathematics, Belgrade, Serbia), aleksandar.kartelj@gmail.com
Grbić Milana (University of Banjaluka, Faculty of Natural Science and Mathematics, Banjaluka, Bosnia and Herzegovina), milana.grbic@pmf.unibl.org
Matić Dragan (University of Banjaluka, Faculty of Natural Science and Mathematics, Banjaluka, Bosnia and Herzegovina), dragan.matic@pmf.unibl.org
Filipović Vladimir (University of Belgrade, Faculty of Mathematics, Belgrade, Serbia), vladofilipovic@hotmail.com
In this paper we study the Roman domination number of some classes of planar
graphs - convex polytopes: An, Rn and Tn. We establish the exact values of
Roman domination number for: An, R3k, R3k+1, T8k, T8k+2, T8k+3, T8k+5 and
T8k+6. For R3k+2, T8k+1, T8k+4 and T8k-1 we propose new upper and lower
bounds, proving that the gap between the bounds is 1 for all cases except
for the case of T8k+4, where the gap is 2.
Keywords: Roman domination number, Convex polytopes