Di-Forcing Polynomials for Cyclic Ladder Graphs CLn

Abstract

The cyclic ladder graph CLn is the Cartesian product of cycles Cn and paths P2, that is CLn=Cn×P2, (n≥3). The di-forcing polynomial of CLn is a binary enumerative polynomial of all perfect matching forcing and anti-forcing numbers. In this paper, we derive recursive formulas for the di-forcing polynomial of cyclic ladder graph CLn by classifying and counting the matching cases of the associated edges of a given vertex, from which we obtain the number of perfect matching, the forcing and anti-forcing polynomials, and the generating function and by computing some di-forcing polynomials of the lower order CLn.