TY - JOUR
T1 - Improved Bounds on the k-tuple (Roman) Domination Number of a Graph
AU - Abd Aziz, Noor A’lawiah
AU - Henning, Michael A.
AU - Rad, Nader Jafari
AU - Kamarulhaili, Hailiza
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.
PY - 2022/6
Y1 - 2022/6
N2 - In Henning and Jafari Rad (Graphs Combin, 37: 325–336, 2021), several new probabilistic upper bounds are given on the k-tuple domination number, k-domination number, Roman domination number, and Roman k-domination number of a graph using the well-known Brooks’ Theorem for vertex coloring, improving all of previous given bounds for the above domination variants. In this paper, we use the well-known Turán’s Theorem, and give a slight improvement of all above given bounds.
AB - In Henning and Jafari Rad (Graphs Combin, 37: 325–336, 2021), several new probabilistic upper bounds are given on the k-tuple domination number, k-domination number, Roman domination number, and Roman k-domination number of a graph using the well-known Brooks’ Theorem for vertex coloring, improving all of previous given bounds for the above domination variants. In this paper, we use the well-known Turán’s Theorem, and give a slight improvement of all above given bounds.
KW - Roman domination
KW - Roman k-tuple domination
KW - Turán’s Theorem
KW - k-domination
KW - k-tuple domination
UR - http://www.scopus.com/inward/record.url?scp=85126836217&partnerID=8YFLogxK
U2 - 10.1007/s00373-022-02471-5
DO - 10.1007/s00373-022-02471-5
M3 - Article
AN - SCOPUS:85126836217
SN - 0911-0119
VL - 38
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
IS - 3
M1 - 75
ER -