iL/i(0, 1)-Labelling of Cactus Graphs

摘要

An L(0,1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that the difference between the labels assigned to any two adjacent vertices is at least zero and the difference between the labels assigned to any two vertices which are at distance two is at least one. The span of an L(0,1)-labelling is the maximum label number assigned to any vertex of G. The L(0,1)-labelling number of a graph G, denoted by λ0.1(G) is the least integer k such that G has an L(0,1)-labelling of span k. This labelling has an application to a computer code assignment problem. The task is to assign integer control codes to a network of computer stations with distance restrictions. A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we label the vertices of a cactus graph by L(0,1)-labelling and have shown that, △-1≤λ0.1(G)≤△ for a cactus graph, where △ is the degree of the graph G.