Arts and Sciences
Mathematics and Statistics
An L(4, 3, 2, 1)-labeling of a vertex-edge graph G is a function f that assigns either 0 or a specific positive integer as a label to each vertex with the following condition: given 2 vertices, the sum of the difference of their labels and their distance in the graph must be at least 5. Symbolically: |f(u) − f(v)| + d(u, v) ≥ 5 if u ≠ v. The L(4, 3, 2, 1)-labeling number of a vertex-edge graph G is the smallest positive integer k, such that the condition previously stated is followed, and there is no label greater than k. In this paper, we show the L(4, 3, 2, 1)-labeling number of several types of graphs including cycles, paths, spider graphs, stars, and some caterpillars.
Reyes, Hector G. and Iselin, Samuel, "L(4,3,2,1) labeling" (2017). Symposium on Undergraduate Research and Creative Expression (SOURCE). 617.