Base Polynomials for Degree and Distance Based Topological Invariants of N-Bilinear Straight Pentachain

Abstract

Degree and distance-based graph polynomials are important not only as graph invariants but also for their applications in physics, chemistry, and pharmacy. The present paper is concerned with the Hosoya and Schultz polynomials of n-bilinear straight pentachain. It was observed that computing these polynomials directly by definitions is extremely difficult. Thus, we follow the divide and conquer rule and introduce the idea of base polynomials. We actually split the vertices into disjoint classes and then wrote the number of paths in terms of polynomials for each class, which ultimately serve as bases for Hosoya and Schultz polynomials. We also recover some indices from these polynomials. Finally, we give an example to show how these polynomials actually work.