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An L(3,2,1)-labeling for the graph G=(V,E) is an assignment f of a label to each vertices of G such that |f(u)?f(v)|≥4?k when dist(u,v)=k≤3. The L(3,2,1)-labeling number, denoted by λ3,2,1(G), for G is the smallest number N such that there is an L(3,2,1)-labeling for G with span N.
In this paper, we compute the L(3,2,1)-labeling number λ3,2,1(G) when G is a cylindrical grid, which is the cartesian product Pm?Cn of the path and the cycle, when m≥4 and n≥138. Especially when n is a multiple of 4, or m=4 and n is a multiple of 6, then we have λ3,2,1(G)=11. Otherwise λ3,2,1(G)=12.
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참고문헌 (18)
참고문헌 신청
A. A. Bertossi / 2003 / Channel assignment with separation for inter-ference avoidence in weierless networks / IEEE Trans. Parall. Distrib. Syst 14:222~235
A. A. Bertossi / 200 / Approximate L-coloring of trees and interval graphs / Networks 49(3):204~216
A. A. Bertossi / 2000 / E cient use of Radio spectrum in weierless networks with channel separation between close stations, dial M for mobility / International ACM workshop, Discrete algorithms and methods for mobile computing
T. Calamoneri / 2006 / The L(h; k)-labeling problem: A survey and annotated bibliogra-phy / Comp. J 49:585~608
T. Calamoneri / 2011 / The L(h; k)-Labelling Problem: An Updated Survey and Anno-tated Bibliography / Comp. J 54:1344~1371
A. A. Bertossi / 200 / Approximate L-coloring of trees and interval graphs / Networks 49(3):204~216
A. A. Bertossi / 2000 / E cient use of Radio spectrum in weierless networks with channel separation between close stations, dial M for mobility / International ACM workshop, Discrete algorithms and methods for mobile computing
T. Calamoneri / 2006 / The L(h; k)-labeling problem: A survey and annotated bibliogra-phy / Comp. J 49:585~608
T. Calamoneri / 2011 / The L(h; k)-Labelling Problem: An Updated Survey and Anno-tated Bibliography / Comp. J 54:1344~1371
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