Sains Malaysiana 45(1)(2016): 55–58

Orderings a Class of Unicyclic Graphs with Respect to Hosoya and Merrifield-Simmons Index

(Tertib Kelas Graf Unisiklik Indeks Hosoya dan Merrifield-Simmons)

WANG YAN-FENG* & MA NING

School of Mathematics and Computer Science, Northwest University for Nationalities

Lanzhou 730030, China

Diserahkan: 7 Julai 2014/Diterima: 12 November 2014

ABSTRACT

Hosoya and Merrifield-Simmons index were the two valuable topological indices in chemical graph theory. The Hosoya and Merrifield-Simmons index of the class of unicyclic graphs G(k) were investigated, according to the distance between u and v on Cm, their orderings with respect to these two topological indices were obtained.

Keywords: Hosoya index; Merrifield-Simmons index; ordering; unicyclic graph

ABSTRAK

Indeks Hosoya dan Merrifield - Simmons adalah dua indeks topologi penting dalam teori graf kimia. Indeks Hosoya dan Merrifield - Simmons daripada kelas graf unisiklik G(k) dikaji mengikut jarak antara u dan v ke atas Cm, tertib mereka mengikut kedua-dua indeks topologi diperoleh.

Kata kunci: Graf unisiklik; indeks Hosoya; indeks Merrifield-Simmons; tertib

RUJUKAN

Bondy, J.A. & Murty, U.S.R. 1976. Graph Theory with Applications. New York: Macmillan.

Gutman, I. & Polansky, O.E. 1986. Mathematical Concepts in Organic Chemistry. Berlin: Springer.

Hosoya, H. 1971. Topological index, a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbon. Bulletin of Chemical Society of Japan 44: 2332-2339.

Merrifield, R.E. & Simmons, H.E. 1989. Topological Methods in Chemistry. New York: Wiley Sons Inc.

Prodinger, H. & Tichy, R.F. 1982. Fibonacci numbers of graphs. The Fibonacci Quarterly 20: 16-21.

Ser Lee Loh, Shaharuddin Salleh & Nor Haniza. 2014. Linear-time heuristic partitioning technique for mapping of connected graphs into single-row networks Sains Malaysiana 43(8): 1263-1269.

Trinajstic, N. 1992. Chemical Graph Theory. Boca Raton: CRC Press.

Wagner, S.G. 2007. Extremal trees with respect to Hosoya index and Merrifield-Simmons index. MATCH Communications in Mathematical and Computer Chemistry 57(1): 221-233.

Yali, Y., Xiangfeng, P. & Huiqing, P. 2008. Ordering unicyclic graphs with respect to Hosoya indices and Merrifield- Simmons indices. MATCH Communications in Mathematical and Computer Chemistry 59: 191-202.

Zheng, Y., Huiqing, L. & Liu, H. 2008. The maximal merrifield-simmons indices and minimal Hosoya indices of unicyclic graphs. MATCH Communications in Mathematical and Computer Chemistry 59: 157-170.

Ziwen, H., Shubo, C. & Hanyuan, D. 2011. The Merrifield- Simmons index of acyclic molecular graphs. MATCH Communications in Mathematical and Computer Chemistry 66: 825-836.

*Pengarang untuk surat-menyurat; email: wangyanfeng52@163.com