Base Polynomials for Schultz Invariants of Linear Phenylenes

2020/08/11 by Abdul Rauf Nizami, Nizami, Abdul Rauf, Muhammad Aslam Malik +3
Chemistry · Computer Science · Mathematics · #05C12 (Primary) 05C07 #05C31 (Secondary) #Combinatorics (math.CO) #Computational Drug Discovery Methods #FOS: Mathematics #Graph theory and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.2008.04596

openalex publication_date 2020/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L_n be the molecular graph of linear [n]phenylene, and L'_n the graph obtained by attaching 4-membered cycles to terminal hexagons of L_n-1. Thus, L'_n is the molecular graph of the α,ω - dicyclobutadieno derivative of [n-1]phenylene, containing n-1 hexagons and n squares. In this paper we give polynomials which serve as bases for Schultz invariants. Actually, we represent lengths of paths among vertices of degrees 2-2, 2-3, and 3-3 of L_n and L'_n in terms of polynomials, which are used to find Schultz polynomial, modified Schultz polynomial, Schultz index, and modified Schultz index.

Citations

• Selected properties of the Schultz molecular topological index
• Topological organic chemistry. 1. Graph theory and topological indices of alkanes

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