A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä

ON (r,<= 2)-LOCATING-DOMINATING CODES IN THE INFINITE KING GRID




TekijätPelto M

KustantajaAMER INST MATHEMATICAL SCIENCES

Julkaisuvuosi2012

JournalAdvances in Mathematics of Communications

Tietokannassa oleva lehden nimiADVANCES IN MATHEMATICS OF COMMUNICATIONS

Lehden akronyymiADV MATH COMMUN

Numero sarjassa1

Vuosikerta6

Numero1

Aloitussivu27

Lopetussivu38

Sivujen määrä12

ISSN1930-5346

DOIhttps://doi.org/10.3934/amc.2012.6.27


Tiivistelmä
Assume that G = (V, E) is an undirected graph with vertex set V and edge set E. The ball B-r(v) denotes the vertices within graphical distancerfromv. Let I-r(F) = U-v is an element of F(Br(v) boolean AND C)be a set of code words in the neighbourhoods of vertices v is an element of F. A subset C subset of V is called an (r, <= l)-locating-dominating code of type A if sets I-r(F-1) and I-r(F-2) are distinct for all subsets F-1, F-2 subset of V where F-1 not equal F-2, F-1 boolean AND C = F-2 boolean AND C and vertical bar F-1 vertical bar, vertical bar F-2 vertical bar <= l. A subset C subset of V is an (r, <= l)-locating-dominating code of type B if the sets I-r(F) are distinct for all subsets F subset of V\C with at most l vertices. We study (r, <= l)-locating-dominating codes in the infinite king grid when r >= 1 and l = 2. The infinite king grid is the graph with vertex set Z(2) and edge set {{(x(1),y(1)),(x(2),y(2))}parallel to x(1) - x(2)vertical bar <= 1,vertical bar y(1) - y(2)vertical bar <= 1,(x(1),y(1))not equal(x(2),y(2))}.


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