Hosoya Polynomial of Graphs Belonging to Twist Knots

Year 2018, Volume: 10, 38 - 42, 29.12.2018

Abdulgani Şahin , Bünyamin Şahin

Abstract

There is a deep relationship between knot theory and graph theory. Graphs are effective tools for studies into knot theory. It is possible to switch between the two theories by forming the graphs of knots. Thus, the study areas of the two theories meet on a common ground. In this study, we firstly introduce Hosoya polynomial and we work out the Hosoya polynomials for graphs of twist knots which are one of interesting families of knots

and try to get a generalization for them.

Keywords

Twist knots , Knot graph , Hosoya polynomial

References

• Deutsch, E., Klavzar, S., Computing Hosoya polynomials of graphs from primary subgraphs, MATCH Communications in Mathematical and in Computer Chemistry, 70(2)(2013), 627–644.
• Deutsch, E., Klavzar, S., The Hosoya polynomial of distance-regular graphs, Discrete Applied Mathematics, 178(2014), 153–156.
• Farahani, M.R., On the Schultz polynomial and Hosoya polynomial of circumcoronene series of benzenoid, Journal Applied Mathematics & Informatics, 31(2)(2013), 595–608.
• Johnson, I., Henrich, A.K., A Interactive Introduction to Knot Theory, Dover Publications, Inc., Mineola, New York, 2017.