# Bus Route Method and Isomorphism

Event

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.

## Share

COinS

Apr 12th, 10:00 AM Apr 12th, 11:00 AM

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.