Given Zp where p is an integer prime, let's de ne G(k) p to be the digraph whose set of vertices is Zp such that there is a directed edge from a vertex a to a vertex b if ak b mod p. First, we nd our own way to decide ...

Our work continues a long tradition in graph theory studying the relation- ship between vertex connectivity, edge connectivity, and minimum degree. [From Introduction]

This is the fourth and nal thesis that concludes ProfessorWayne M. Dymacek's research project Realizability of n-Vertex Graphs with Prescribed Vertex Connectivity, Edge Connectivity, Minimum Degree, and Maximum Degree. ...

In this thesis we will examine progressions in permutations. We will analyze regular and circular permutations with progressions either modular or regular with rise one or two. We will calculate the number of permutations ...

Steinhaus graphs have many interesting properties, yet there are many things about them that are not yet known. In [1], a formula was discovered for the total number of Steinhaus graphs on 11 vertices with at least one ...

Runs in permutations and similar topics have been studied by various authors under different names. Hegarty examined permutations of finite abelian groups which avoid what he called progressions. Riordan studied 3-runs ...

In this thesis, we investigate sequences defined by linear recurrence relations. These are sequences whose subsequent terms are generated using some linear combination of the previous terms. We call the equation that ...