Labeling Graphs with Two Distance-Constraints

• Main Authors: Chun-Liang Lin, 林俊良
• Other Authors: D.Kuo
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/38557388216266771649

碩士 === 國立東華大學 === 應用數學系 === 90 === Given a graph G, an L(d_{1},d_{2};p,q)-labeling of G is a function f:V(G)-->{0,1,2,...,n} such that |f(u)-f(v)|>= p if d_{G}(u,v)<= d_{1} and |f(u)-f(v)|>= q if d_{G}(u,v)<= d_{2}. A k-L(d_{1},d_{2};p,q)-labeling is an L(d_{1},d_{2};p,q)-labeling f such that max_{vin V(G)}f(v)<= k.The L(d_{1},d_{2};p,q)-labeling number of G, denoted by lambda_{d_{1},d_{2}}^{p,q}(G), is the smallest number k such that G has a k-L(d_{1},d_{2};p,q)-labeling. In this thesis, we give the upper bound and lower bound of the L(d_{1},d_{2};p,q)-labeling number for general graphs and some special graphs. We also discuss L(d_{1},d_{2};p,q)-labeling number of G, when G is a paths.