Permanents of Hexagonal and Armchair Chains
The permanent is important invariants of a graph with some applications in physics. If G is a graph with adjacency matrix A=aij, then the permanent of A is defined as permA=∑σ∈Sn∏i=1naiσi, where Sn denotes the symmetric group on n symbols. In this paper, the general form of the adjacency matrices of...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/7786922 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The permanent is important invariants of a graph with some applications in physics. If G is a graph with adjacency matrix A=aij, then the permanent of A is defined as permA=∑σ∈Sn∏i=1naiσi, where Sn denotes the symmetric group on n symbols. In this paper, the general form of the adjacency matrices of hexagonal and armchair chains will be computed. As a consequence of our work, it is proved that if Gk and Hk denote the hexagonal and armchair chains, respectively, then permAG1=4, permAGk=k+12, k≥2, and permAHk=4k with k≥1. One question about the permanent of a hexagonal zig-zag chain is also presented. |
|---|---|
| ISSN: | 1687-0425 |