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Abstract
Let G be a connected graph, and let D(G) be the set of all dominating (multi)sets for G. For D_{1} and D_{2} in D(G), we say that D_{1} is singlestep transferable to D_{2} if there exist u∈D_{1} and v∈D_{2}, such that uv∈E(G) and D_{1}−{u}=D_{2}−{v}. We write D_{1}⟶∗D_{2} if D_{1} can be transferred to D_{2} through a sequence of singlestep transfers. We say that G is ktransferable if D_{1}⟶∗D_{2} for any D_{1},D_{2}∈D(G) with D_{1}=D_{2}=k. The transferable domination number of G is the smallest integer k to guarantee that G is ltransferable for all l≥k. We study the transferable domination number of graphs in this paper. We give upper bounds for the transferable domination number of general graphs and bipartite graphs, and give a lower bound for the transferable domination number of grids. We also determine the transferable domination number of P_{m}×P_{n} for the cases that m=2,3, or mn≡0(mod6). Besides these, we give an example to show that the gap between the transferable domination number of a graph G and the smallest number k so that G is ktransferable can be arbitrarily large.
Original language  English 

Pages (fromto)  135146 
Number of pages  12 
Journal  Discrete Applied Mathematics 
Volume  313 
DOIs  
State  Published  31 May 2022 
Keywords
 Dominating set
 Domination number
 Grid
 Transferable domination number
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Dive into the research topics of 'Transferable domination number of graphs'. Together they form a unique fingerprint.Projects
 1 Finished

The Study of Blocking Dominating Sets and Related Labeling Problems on Cartesian Product of Graphs
1/08/19 → 31/07/20
Project: Research