廣義彼得森圖的(2,1)-全標號

Abstract

Let G = (V,E) be a graph. A (2,1)-total labeling of G is a mapping l from V∪E into {0,...,λ}, for some integer λ, such that: (i) if x and y are adjacent vertices then l(x)≠l(y), (ii) if e and f are adjacent edges then l(e)≠l(f), (iii) if an edge e is incident to a vertex x then |l(x)-l(e)|≧2. The minimum λ for which G has a (2,1)-total labeling into {0,...,λ} is denoted by λ^T_2(G). Let n and k be two positive integers. The graph with vertices {u_1,...,u_n} and {v_1,...,v_n} and edges u_iu_(i+1), u_iv_i and v_iv_(i+k), where addition is modulo n is called generalized Petersen graph and denoted by P(n,k). In this thesis, we mainly focus on the (2,1)-total labeling of cubic graphs and we obtain some results for the generalized Petersen graphs.