Interference between radio signals can be modeled using distance labeling where the vertices on the graph represent the radio towers and the edges represent the interference between the towers. The distance between vertices affects the labeling of the vertices to account for the strength of interference. In this paper we consider three levels of interference between signals on a given graph, G. Define D(x,y) to represent the distance between vertex x and vertex y. An L(d,j,s) labeling of graph G is a function f from the vertex set of a graph to the set of positive integers, where |f(x)-f(y)| ³ d if D(x,y)=1, |f(x)-f(y)|³ j if D(x,y)=2, and |f(x)-f(y)|³ s if D(x,y)=3 for positive integers m and d where d>j>s. In this paper we will examine surjective and minimal labeling of different families of graphs including paths, cycles, caterpillars, complete graphs, and complete bipartite graphs.
Debra Czarneski, Department of Mathematics, Simpson College firstname.lastname@example.org
Lingscheit, Michelle; Ruff, Kiersten; and Ward, Jeremy
"L(d,j,s) Minimal and Surjective Graph Labeling,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 10
, Article 12.
Available at: https://scholar.rose-hulman.edu/rhumj/vol10/iss1/12