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Browsing Auburn Theses and Dissertations by Author "Johnson, Peter D., Jr."
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Disjoint Intersection Problem For Steiner Triple Systems
Srinivasan, Sangeetha (2007-12-15)
Let (S, T_1) and (S, T_2) be two Steiner Triple systems on the set S of symbols with the set of triples T_1 and T_2 respectively. They are said to intersect in m blocks if |T_1 intersection T_2| = m. Further, if the blocks ...
On the existence of even and k-divisible-matchings
Moore, Emilia (2008-05-15)
The concept of an an even matching was first introduced by Billington and Hoffman.
They were used to find gregarious 4-cycle decompositions of $K_{8t(a),b}$ with a and b odd.
Their paper contains even matchings of type ...
Security and secure-dominating sets in graphs
Jones, Cadavious (2014-04-29)
All graphs in this paper are finite and simple. Let G = (V;E) be a graph, x an element of V and
S a subset of V. Following convention, we let N(x) := {u : where ux is an element of E} and N[x] := {x}union N(x). For
S, ...
Topics in Edge Regular Graphs
Bragan, Kelly (2014-07-24)
A graph, G, is edge-regular with parameters (n,d,lambda) if G is regular of degree d on n vertices and for all u, v in V(G) such that uv is in E(G), the order of the intersection of N(u) and N(v) is lambda, where N(v) ...