L(p,q)-Labeling of Digraphs

• Main Authors: Yi-Ting Chen, 鄭伊婷
• Other Authors: David Kuo
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/16567390284638302822

碩士 === 國立東華大學 === 應用數學系 === 91 === Given a graph G and two positive integers p, q with p > q an L(p, q)-labeling of G is a function f from the vertex set V (G) to the set of all nonnegative integers such that |f(x)−f(y)|>p if d_G(x,y)=1 and |f(x)-f(y)|> q if d_G(x,y)=2. A k-L(p, q)-labeling is an L(p, q)-labeling such that no label is greater than k. The L(p, q)-labeling number of G, denoted by λ_{p,q}(G) is the smallest number k such that G has a k-L(p, q)-labeling. When consider the digraph D, we use λ^*_{p,q}(D) in place of λ_{p,q}(D). we study the L(p, q)-labeling number of a digraph D in this thesis, we find some relations between the L(p, q)-labeling number of a graph G and an orientation D of G, and give some results for the L(p, q)-labeling numbers of k-partite digraphs. We also study the L(p, q)-labeling numbers for those graphs D for which the underlying graph are paths, cycle or trees.