Hosoya Polynomial of Graphs Belonging to Twist Knots

ISSN: 2148-1830
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: MATEMATİKÇİLER DERNEĞİ

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

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[1] 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.
[2] Deutsch, E., Klavzar, S., The Hosoya polynomial of distance-regular graphs, Discrete Applied Mathematics, 178(2014), 153–156.
[3] Farahani, M.R., On the Schultz polynomial and Hosoya polynomial of circumcoronene series of benzenoid, Journal Applied Mathematics & Informatics, 31(2)(2013), 595–608.
[4] Johnson, I., Henrich, A.K., A Interactive Introduction to Knot Theory, Dover Publications, Inc., Mineola, New York, 2017.
[1] 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. 1 [2] Deutsch, E., Klavzar, S., The Hosoya polynomial of distance-regular graphs, Discrete Applied Mathematics, 178(2014), 153–156. 1, 1.1 [3] Farahani, M.R., On the Schultz polynomial and Hosoya polynomial of circumcoronene series of benzenoid, Journal Applied Mathematics & Informatics, 31(2)(2013), 595–608. 1 [4] Johnson, I., Henrich, A.K., A Interactive Introduction to Knot Theory, Dover Publications, Inc., Mineola, New York, 2017. 1.2