Upper Bound for the Domination Number of Cylindrical Grid Graph P8Cn

2017 ◽  
Vol 14 (9) ◽  
pp. 4255-4260
Author(s):  
Qiong Kang ◽  
Xiujun Zhang
Keyword(s):  
Upper Bound ◽  
Domination Number ◽  
Grid Graph ◽  
Cylindrical Grid

scholarly journals Bounds on the Size of the Minimum Dominating Sets of Some Cylindrical Grid Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Mrinal Nandi ◽  
Subrata Parui ◽  
Avishek Adhikari
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Domination Number ◽  
Cartesian Product ◽  
Wireless Sensor ◽  
Dominating Sets ◽  
Grid Graph ◽  
Grid Graphs ◽  
Cylindrical Grid ◽  
Domination Numbers

Let γPm □ Cn denote the domination number of the cylindrical grid graph formed by the Cartesian product of the graphs Pm, the path of length m, m≥2, and the graph Cn, the cycle of length n, n≥3. In this paper we propose methods to find the domination numbers of graphs of the form Pm □ Cn with n≥3 and m=5 and propose tight bounds on domination numbers of the graphs P6 □ Cn, n≥3. Moreover, we provide rough bounds on domination numbers of the graphs Pm □ Cn, n≥3 and m≥7. We also point out how domination numbers and minimum dominating sets are useful for wireless sensor networks.

scholarly journals An upper bound on the domination number of n-vertex connected cubic graphs

2009 ◽  
Vol 309 (5) ◽  
pp. 1142-1162 ◽  
Author(s):  
A.V. Kostochka ◽  
B.Y. Stodolsky
Keyword(s):  
Upper Bound ◽  
Domination Number ◽  
Cubic Graphs

A note on improved upper bounds on the transversal number of hypergraphs

2019 ◽  
Vol 11 (01) ◽  
pp. 1950004
Author(s):  
Michael A. Henning ◽  
Nader Jafari Rad
Keyword(s):  
Upper Bound ◽  
Dominating Set ◽  
Domination Number ◽  
Minimum Size ◽  
Total Domination ◽  
Total Domination Number ◽  
Minimum Cardinality ◽  
Total Dominating Set ◽  
Isolated Vertex ◽  
Transversal Number

A subset [Formula: see text] of vertices in a hypergraph [Formula: see text] is a transversal if [Formula: see text] has a nonempty intersection with every edge of [Formula: see text]. The transversal number of [Formula: see text] is the minimum size of a transversal in [Formula: see text]. A subset [Formula: see text] of vertices in a graph [Formula: see text] with no isolated vertex, is a total dominating set if every vertex of [Formula: see text] is adjacent to a vertex of [Formula: see text]. The minimum cardinality of a total dominating set in [Formula: see text] is the total domination number of [Formula: see text]. In this paper, we obtain a new (improved) probabilistic upper bound for the transversal number of a hypergraph, and a new (improved) probabilistic upper bound for the total domination number of a graph.

An upper bound on the double Roman domination number

2018 ◽  
Vol 36 (1) ◽  
pp. 81-89 ◽  
Author(s):  
J. Amjadi ◽  
S. Nazari-Moghaddam ◽  
S. M. Sheikholeslami ◽  
L. Volkmann
Keyword(s):  
Upper Bound ◽  
Domination Number ◽  
Roman Domination ◽  
Roman Domination Number ◽  
Double Roman Domination

scholarly journals An upper bound on the domination number of a graph with minimum degree 2

2009 ◽  
Vol 309 (4) ◽  
pp. 639-646 ◽  
Author(s):  
Allan Frendrup ◽  
Michael A. Henning ◽  
Bert Randerath ◽  
Preben Dahl Vestergaard
Keyword(s):  
Upper Bound ◽  
Minimum Degree ◽  
Domination Number

THE DOMINATION NUMBER OF STRONG PRODUCT OF DIRECTED CYCLES

2014 ◽  
Vol 06 (02) ◽  
pp. 1450021
Author(s):  
HUIPING CAI ◽  
JUAN LIU ◽  
LINGZHI QIAN
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Domination Number ◽  
Strong Product ◽  
Directed Cycles

Let γ(D) denote the domination number of a digraph D and let Cm ⊗ Cn denote the strong product of Cm and Cn, the directed cycles of length m, n ≥ 2. In this paper, we determine the exact values [Formula: see text] Furthermore, we give a lower bound and an upper bound of γ(Cm1 ⊗ Cm2 ⊗ ⋯ ⊗ Cmn) and obtain that [Formula: see text] when at least n-2 integers of {m1, m2, …, mn} are even (because of the isomorphism, we assume that m3, m4, …, mn are even).

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