# 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.