Counting Multigraph Pairs of λKn
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.
O'Connor, William A., "Counting Multigraph Pairs of λKn" (2017). Honors Projects. 23.