Scott Herlein

Date of Defense

Spring 4-12-2004



First Advisor

Ping Zhang, Mathematics

Second Advisor

Paul Eenigenburg, Mathematics

Third Advisor

Christine Browning, Mathematics


directed graphs (digraphs)


Let D be an oriented graph of order n and size m. A Ɣ-labeling of D is a one-to-one function f' : V(D) → {0,1,2,...,m} that induces a labeling f' : E(D) → {±1,±2,...,±m} of the arcs of D defined by f'(e) = f(v) - f(u) for each arc e = (u,v) of D. The value of a Ɣ-labeling f is val(f) = ∑eE(G)f'(e). A Ɣ-labeling of D is balanced if the value of f is 0. A Ɣ-labeling of D graceful if the induced edge-labeling f' is also one-to-one. An oriented graph D is balanced if D has a balanced labeling. A graph G is orientably balanced if G has a balanced orientation. In this project, we study the properties of balanced Ɣ-labelings of oriented graphs and orientably balanced graphs.

Access Setting

Honors Thesis-Campus Only