Anti-Forcing Number of Certain k-Circumscribed Peri-Condensed Benzenoid Graphs

Abstract

The concept of Kekulé structure (chemically) and perfect matching (mathematically) in a molecular graph G are analogous. A matching M in a graph G is a collection of independent edges in G and is interpreted to be perfect if every single vertex of G is incident with one and only one edge in M. An anti-forcing set S of edges or covalent bonds of G is considered to be present if the removal of S leaves the graph G with a unique perfect matching or Kekulé structure. The anti-forcing set S with the minimal cardinality is referred to as the minimum anti-forcing set, and its cardinality can be expressed as af (G). The anti-forcing number of k-circumscribed peri-condensed benzenoid graphs and certain circum-peri-condensed sheets were investigated and determined in this manuscript.