A patch is a plane graph whose boundary is an elementary circuit with only vertices of degree 2 or 3, with all degree-2 vertices restricted to the boundary. A Kekulé structure for a patch is a perfect matching. Not all patches admit a perfect matching; in this paper, we define internal Kekulé structures, which match all degree-3 vertices but not necessarily all degree-2 vertices. We consider internal Kekulé structures for general patches to determine what properties of Kekulé structures on hexagonal or graphene patches can be generalized to arbitrary patches, and when a graphene patch with a few defective (non-hexagonal) faces in the interior still "behaves like graphene" away from the defects.
|Original language||English (US)|
|Number of pages||13|
|State||Published - 2016|
ASJC Scopus subject areas
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics