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Abstract

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.

Author Bio

The work was completed June through August 2008 during the Dr. Albert H. & Greta A. Bryan Summer Research Program at Simpson College, under the supervision of Dr. Debra Czarneski. The work was also presented at MathFest in Madison, Wisconsin in August 2008. Michelle Lingscheit is currently in her sophomore year as a mathematics and chemistry double major, and is planning on earning her Ph.D. in either chemistry or mathematics.

The work was completed June through August 2008 during the Dr. Albert H. & Greta A. Bryan Summer Research Program at Simpson College, under the supervision of Dr. Debra Czarneski. The work was also presented at MathFest in Madison, Wisconsin in August 2008. Kiersten Ruff is currently in her sophomore year as a mathematics and physics double major and plans on attending graduate school in mathematics.

The work was completed June through August 2008 during the Dr. Albert H. & Greta A. Bryan Summer Research Program at Simpson College, under the supervision of Dr. Debra Czarneski. The work was also presented at MathFest in Madison, Wisconsin in August 2008. Jeremy Ward is currently in his junior year as a mathematics and physics double major and plans on attending graduate school in physics.

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