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Abstract

We use combinatorial knot theory to construct invariants for spatial graphs. This is done by performing certain replacements at each vertex of a spatial graph diagram D , which results in a collection of knot and link diagrams in D. By applying known invariants for classical knots and links to the resulting collection, we obtain invariants for spatial graphs. We also show that for the case of undirected spatial graphs, the invariants we construct here satisfy a certain contraction-deletion recurrence relation.

Author Bio

Elaina Aceves graduated Magna Cum Laude from California State University, Fresno in 2014 majoring in mathematics. She began work on this paper in the fall of 2012 after taking a topics course about knot theory that semester. Elaina presented this research at the Underrepresented Students in Topology and Algebra Research Symposium (USTARS) and the National Conference for Undergraduate Women in Math (NCUWM). She is currently a masters mathematics student and a part time lecturer at California State University, Fresno.

Jennifer Elder graduated Cum Laude from California State University, Fresno in 2014, where she majored in Mathematics. Her work on this paper began in the Fall of 2012 in an Introduction to Knot Theory course. She is currently a Mathematics Masters student at California State University, Fresno, where she is doing research in Abstract Algebra.

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