Bus Route Method and Isomorphism
Submission Type
Event
Expected Graduation Date
2015
Location
Room E102, Center for Natural Sciences, Illinois Wesleyan University
Start Date
4-12-2014 10:00 AM
End Date
4-12-2014 11:00 AM
Disciplines
Applied Mathematics
Abstract
Two simple graphs, G and H, each of which have n vertices (with n a positive integer greater than 3) are called a graph pair of order n if the following three conditions all hold: (1) G and H union to the complete graph, (2) G and H have no isolated vertices, and (3) G is not isomorphic to H. Graph pairs of order 4 and 5 have been classified. This research took a step further to find graph pairs of order 6. During the finding, I discover the Bus Route method to make sure two graphs are not isomorphic. Two graphs G and H are said to be isomorphic if there exists a bijection, f, between the vertices of G and the vertices of H such that for every pair of vertices u and v in V(G), uv is an edge of G if and only if f(u)f(v) is an edge of H. The Bus Route method is based on the definition of isomorphism.
Bus Route Method and Isomorphism
Room E102, Center for Natural Sciences, Illinois Wesleyan University
Two simple graphs, G and H, each of which have n vertices (with n a positive integer greater than 3) are called a graph pair of order n if the following three conditions all hold: (1) G and H union to the complete graph, (2) G and H have no isolated vertices, and (3) G is not isomorphic to H. Graph pairs of order 4 and 5 have been classified. This research took a step further to find graph pairs of order 6. During the finding, I discover the Bus Route method to make sure two graphs are not isomorphic. Two graphs G and H are said to be isomorphic if there exists a bijection, f, between the vertices of G and the vertices of H such that for every pair of vertices u and v in V(G), uv is an edge of G if and only if f(u)f(v) is an edge of H. The Bus Route method is based on the definition of isomorphism.