Document Type
Article
Journal/Book Title/Conference
Mathematics
Volume
7
Issue
4
Publisher
M D P I AG
Publication Date
3-28-2019
First Page
1
Last Page
6
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Abstract
A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k−1. A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of a union of graphs is the union of their images and if it maps the edgeless graph to the edgeless graph. We investigate linear operators on the set of graphs on n vertices that map graphs of genus k to graphs of genus k and graphs of genus k+1 to graphs of genus k +1. We show that such linear operators are necessarily vertex permutations. Similar results with different restrictions on the genus k preserving operators give the same conclusion.
Recommended Citation
Beasley, L.B.; Kim, J.H.; Song, S.-Z. Linear Operators That Preserve the Genus of a Graph. Mathematics 2019, 7, 312.
