  In the branch of mathematics known as graph theory, graphs are considered as
a set of points, called vertices, with connections between these points, called
edges. The purpose of this paper is to study mappings between two graphs that
have certain desirable properties, called graph homomorphisms, and the
probability of such a mapping occurring. By using notions from graph theory and
combinatorics, in this paper we prove several new theorems that place bounds on
this probability for certain common classes of graphs such as Kn, and show that
isolated vertices may safely be ignored.
