Title

Counting Multigraph Pairs of λKn

Graduation Year

2017

Comments

At the request of the author, this essay is not available for download. Bona fide researchers may consult it by visiting the University Archives in Tate Archives & Special Collections; contact archives@iwu.edu for details.

Abstract

The purpose of this paper is to count multigraph pairs of λKn, as well as explore various results associated with multigraph pairs.

Let λKn be the complete λ-fold multigraph of order n. Have (G,H) be a λ-fold multigraph pair of order n such that:

1. There are no isolated vertices

2. G ≢ H

3. E(G) U E(H) = λKn

In this paper, we found the number of multigraph pairs of orders 2 and 3 of index λ. Additionally, we were able to find partial results for order 4 of index λ, as well as some relations of multigraphs based on structures of subgraphs of K4, involving counting and coloring.

Disciplines

Mathematics

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