On (4,1)-Total Labelings of Cactus Graphs

• Main Authors: Fu-Mei Han, 韓馥鎂
• Other Authors: Chin-Lin Shiue
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/uv737t

碩士 === 中原大學 === 數學研究所 === 102 === Let G be a graph. A (p,1)-total labeling of G is an assignment of integers to each vertex and edge of G such that any adjacent vertices of G are labeled with distinct integers, any adjacent edges of G are labeled with distinct integers and a vertex and its incident edge receive integers that differ by at least p in absolute value. The span of (p,1)-total labeling of G is the maximum difference between two labels. The minimum span of (p,1)-total labeling of G is called the (p,1)-total number and denote by λ_p^T (G). A cactus graph is a connected graph in which every block is either an edge or a cycle. In this thesis, we focus on the (4,1)-total labeling for the class of cactus graphs containing finite cycles joined with a common cut-vertex and show that for any cactus graph G in this class, λ_p^T (G)=Δ+4 when Δ=4, otherwise λ_p^T (G)=Δ+3 when Δ≥6 where ∆ is the maximum degree of G.