L(4,3,2,1) labeling

Faculty Sponsor

Zsuzsanna Szaniszlo


Arts and Sciences


Mathematics and Statistics

Presentation Type

Poster Presentation

Symposium Date

Spring 5-4-2017


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.

Biographical Information about Author(s)

Samuel Iselin is a sophomore mathematics major from Platteville, Wisconsin. He is the vice president of the Valpo Karate Club and a member of the Social Action Leadership Team at Valparaiso University. Samuel plans to continue research in mathematics throughout his time at Valparaiso University.

Hector Reyes was born and raised in Puerto Rico. Currently, he is part of the track and field team at Valparaiso University and a double major in mathematics and economics. He aspires to earn a Ph.D. in economics after undergraduate school and go back to Puerto Rico to be a professor in economics.

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