Omega and related polynomials of polyomino chains of \(4 k\)-cycles. (English) Zbl 07244494

Alaeiyan, Mehdi; Gilani, Alireza; Mojarad, Rasoul; Asadpour, Jafar

Kuwait J. Sci. 41, No. 1, 85-92 (2014).

Summary: Omega polynomial of a graph \(G\) is defined, on the ground of “opposite edge strips” ops: \(\Omega(G;y)=\sum\limits_c m(G,c)x^c\), where \(m(G,c)\) is the number of ops strips of length \(c\). The Sadhana polynomial \(Sd(G;x)\) can also be calculated by ops counting. In this paper we compute these polynomials for polyomino chains of \(4k\)-cycles. Also by using Omega polynomial we can compute the (edge) PI\(_c\) polynomial for this graph.

MSC:

12	Field theory and polynomials
05	Combinatorics

Keywords:

Omega polynomial; Sadhana polynomial; PI\(_c\) polynomial; strips; polyomino chain