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Automorphism Groups of k-star n-path Saturated Graphs
Li, Shushangxuan
Li, Shushangxuan
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Text, Honors papers, Mathematics and Computer Science, Department of, Student research
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Abstract
In combinatorics, graph theory and Ramsey theory are two rich subjects
of study. There are many directions and problems to pursue. The automorphism
groups of graphs provide a connection between graph theory and
group theory. In this project, we will study a Ramsey-theoretic aspect of
graph theory. The main question is: how many edges must a tree contain
in order to guarantee the presence of a k-star or ann-path? Another way
to think about this problem is: what is the maximum number of edges that
a tree with no k-star or n-path can contain? We will establi..sh a general
formula for the number of edges using induction and classify the trees that
achieve this maximum. In addition, we will describe the automorphism
group of these saturated trees. The same questions will be studied for connected
graphs following a similar procedure. We will show that the number
of edges for connected graphs has a close relation with the one for trees.
Description
Shushangxuan Li granted permission for the digitization of his paper. It was submitted by CD