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Full-Text Articles in Discrete Mathematics and Combinatorics
Average Genus Of The Cube, Jody Koenemann
Average Genus Of The Cube, Jody Koenemann
Honors Theses
In recent years, there has been interest in the mathematical community in a rapidly developing branch of theoretical mathematics known as random topological graph theory. This new area of mathematics explores the different ways in which certain graphs can be imbedded in given surfaces. The random nature of the new branch results when one also imposes a random distribution on set of all imbeddings of a fixed graph, via the orientation of the edges at each vertex. Using the technique of J. Edmonds, developed in 1960, this paper explores the imbeddings for the graph Q3 using a particular group …
Third Order Degree Regular Graphs, Leslie D. Hayes
Third Order Degree Regular Graphs, Leslie D. Hayes
Honors Theses
A graph G is regular of degree d if for every vertex v in G there exist exactly d vertices at distance 1 from v. A graph G is kth order regular of degree d if for every vertex v in G, there exist exactly d vertices at distance k from v. In this paper, third order regular graphs of degree 1 with small order are characterized.
Imbedding Problems In Graph Theory, William Goodwin
Imbedding Problems In Graph Theory, William Goodwin
Honors Theses
For some years there has been interest among mathematicians in determining the different ways in which certain graphs can be imbedded in given surfaces. M.P. VanStraten in 1948, determined that it is possible to imbed the graph K3,3 (which is the graph representing the famous three houses, three utilities problem) in the torus in only two ways. She then used this fact to show that the graph representing the configuration of Desargues (containing K3,3 as a subgraph) has genus two. One major source of motivation for the work on imbedding problems has been their relation to coloring problems …