Minimum Number of Kekulé Structures of Certain Benzenoid Graphs and Pr[m,n]-Polyacenic Nanotubes

Abstract

In a molecular graph, a Kekulé structure and perfect matching resembles the same. Thus, the number of Kekulé structure(chemically) is equal to the number of perfect matching (mathematically) required to cover the edge set or covalent bonds of a molecular graph entirely. The number of possible Kekulé structures in a molecule (benzenoids) is used to describe the extent of its aromatic property and plays an significant role in the analysis of resonance energy and stability of certain chemical compounds. In this article, the minimum number of Kekulé structures (K) that covers all the edges of a class of peri-condensed benzenoid graphs possessing three rows of hexagon of various length and $P^r[m,n]$-polyacenic nanotubes were discussed and summarized.

Keywords:

• Kekulé structures
• perfect matchings
• excessive index
• benzenoid graphs
• t-polyacenic nanotubes

Disclosure statement

No potential conflict of interest was reported by the author(s).