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Wiener Index of Gear Fan Graph and Gear Wheel Graph
Corresponding Author(s) : Wei Gao
Asian Journal of Chemistry,
Vol. 26 No. 11 (2014): Vol 26 Issue 11
Abstract
Chemical compounds and drugs are often modeled as graphs where each vertex represents an atom of molecule and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph and can be different structures. An indicator defined over this molecular graph, the Wiener index, has been shown to be strongly correlated to various chemical properties of the compounds. The Wiener index of a graph is defined as the sum of distances between all pairs of vertices of the graph. It has been found extensive applications in chemistry. In this paper, we determine the Wiener index of gear fan graph, gear wheel graph and their r-corona graphs.
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- L. Yan, Y.F. Li, W. Gao and J.S. Li, J. Chem. Pharm. Res., 5, 260 (2013).
- Y.J. Pan, J. Math. Stu., 42, 280 (2009).
- D.Q. Chen, X. Dong and Z. Fan, J. Wuhan Inst. Chem. Tech., 27, 82 (2012); doi:10.1007/s11595-012-0412-8.
- B.H. Xing and G.X. Cai, OR Tran., 15, 36 (2011).
- H. Wan and H.Z. Ren, J. Math. Stu., 45, 207 (2012).
- Y.J. Pan, J. Math. Stu., 46, 260 (2013).
- D. Stevanovic, Match Commun. Math. Comput. Chem, 60, 71 (2008).
- Y. Hong, H.Q. Liu and X.Y. Wu, Hacet. J. Math. Stat., 40, 63 (2011).
- X.D. Zhang and Q.Y. Xiang, Match Commun. Math. Comput. Chem., 60, 623 (2008).
- G. Cash, S. Klavžar and M. Petkovšek, J. Chem. Inf. Comput. Sci., 42, 571 (2002); doi:10.1021/ci0100999.
- E. Castro, I. Gutman, D. Marino and P. Peruzzo, J. Serb. Chem. Soc., 67, 647 (2002); doi:10.2298/JSC0210647C.
- B. Wu, Match Commun. Math. Comput. Chem., 64, 699 (2010).
- A. Vijayabarathi and G.S.G.N. Anjaneyulu, Int. J. Chem. Tech. Res., 5, 1847 (2013).
- P. Dankelmann, I. Gutman, S. Mukwembi and H.C. Swart, Discrete Math., 309, 3452 (2009); doi:10.1016/j.disc.2008.09.040.
- A.A. Dobrynin, R. Entringer and I. Gutman, Acta Appl. Math., 66, 211 (2001); doi:10.1023/A:1010767517079.
References
L. Yan, Y.F. Li, W. Gao and J.S. Li, J. Chem. Pharm. Res., 5, 260 (2013).
Y.J. Pan, J. Math. Stu., 42, 280 (2009).
D.Q. Chen, X. Dong and Z. Fan, J. Wuhan Inst. Chem. Tech., 27, 82 (2012); doi:10.1007/s11595-012-0412-8.
B.H. Xing and G.X. Cai, OR Tran., 15, 36 (2011).
H. Wan and H.Z. Ren, J. Math. Stu., 45, 207 (2012).
Y.J. Pan, J. Math. Stu., 46, 260 (2013).
D. Stevanovic, Match Commun. Math. Comput. Chem, 60, 71 (2008).
Y. Hong, H.Q. Liu and X.Y. Wu, Hacet. J. Math. Stat., 40, 63 (2011).
X.D. Zhang and Q.Y. Xiang, Match Commun. Math. Comput. Chem., 60, 623 (2008).
G. Cash, S. Klavžar and M. Petkovšek, J. Chem. Inf. Comput. Sci., 42, 571 (2002); doi:10.1021/ci0100999.
E. Castro, I. Gutman, D. Marino and P. Peruzzo, J. Serb. Chem. Soc., 67, 647 (2002); doi:10.2298/JSC0210647C.
B. Wu, Match Commun. Math. Comput. Chem., 64, 699 (2010).
A. Vijayabarathi and G.S.G.N. Anjaneyulu, Int. J. Chem. Tech. Res., 5, 1847 (2013).
P. Dankelmann, I. Gutman, S. Mukwembi and H.C. Swart, Discrete Math., 309, 3452 (2009); doi:10.1016/j.disc.2008.09.040.
A.A. Dobrynin, R. Entringer and I. Gutman, Acta Appl. Math., 66, 211 (2001); doi:10.1023/A:1010767517079.