L(4, 3, 2, 1)-labeling for simple graphs

Abstract

An L(4, 3, 2, 1)-labeling of a graph is a function which assigns label to each vertex of the graph such that if two vertices are one, two, three and four distance apart then assigned labels must have a difference of at least 4, 3, 2 and 1 respectively between them. This paper presents L(4, 3, 2, 1)-labeling number for simple graphs such as complete graphs, complete bipartite graphs, stars, paths and cycles. This paper also presents an L(4, 3, 2, 1)-labeling algorithm for paths which is optimal for paths on n_7 vertices.