Spanning Trees of Complete Graphs and Cycles

John Caughman

Spring 2021

Thesis

Degree Name

Bachelor of Science (B.S.) in Mathematics and University Honors

Department

Mathematics and Statistics

English

Subjects

Spanning trees (Graph theory)

DOI

10.15760/honors.1151

Abstract

Spanning trees are typically used to solve least path problems for finding the minimal spanning tree of a graph. Given a number t ≥ 3 what is the least number n = α(t) such that there exists a graph on n vertices having precisely t spanning trees? Specifically, how will the factoring of t with the use of cycles connected by one vertex affect α(t)? Lower and upper bounds of α(t) are graphed by using properties of cycles and complete graphs. The upper bound of α(t) is then improved by constructing a graph of connected cycles {Cp1, C­p2, Cp3, … , Cpn} where p1, p2, p3 … pn belong to the prime factorization of t. The bounds of α(t) are significantly improved.

Rights

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Persistent Identifier

https://archives.pdx.edu/ds/psu/36145

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