正則圖之(p ,1)-全標號

Abstract

Abstract 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 two 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 a ( 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). In this thesis, we first prove that for each Class 2 △-regular graph G if p≥max⁡{χ+1 ,△}, then λ_P^T (G) ≥ △+p+χ-2. Next, we find some sufficient conditions for a Class 2 △-regular graph G which has the property that if p≥max⁡{χ+1 ,△}, then λ_P^T (G)= △+p+χ-2.