Four new sums of graphs and their Wiener indices. (English) Zbl 1172.05318

Eliasi, Mehdi; Taeri, Bijan

Discrete Appl. Math. 157, No. 4, 794-803 (2009).

Summary: The Wiener index is the sum of distances between all vertex pairs in a connected graph. This notion was motivated by various mathematical properties and chemical applications. In this paper we introduce four new operations on graphs and study the Wiener indices of the resulting graphs.

MSC:

05C12	Distance in graphs
05C90	Applications of graph theory
92E10	Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

Keywords:

Wiener index; distance; operations on graphs

References:

[1]	Althöfer, I., Average distance in undirected graphs and the removal of vertices, J. combin. theory ser. B, 48, 140-142, (1990) · Zbl 0688.05045
[2]	Buckley, F.; Harary, F., Distance in graphs, (1990), Addison-Wesley Redwood, CA · Zbl 0688.05017
[3]	Cvetkocic, D.M.; Doob, M.; Sachs, H., Spectra of graphs theory and application, (1980), Academic Press New York
[4]	Dankelmann, P., Average distance and independence numbers, Discrete appl. math., 51, 75-83, (1994) · Zbl 0803.05020
[5]	Dobrynin, A.A.; Entringer, R.; Gutman, I., Wiener index of trees: theory and applications, Acta appl. math., 66, 211-249, (2001) · Zbl 0982.05044
[6]	Dobrynin, A.A., A simple formula for the calculation of the Wiener index of hexagonal chains, Comput. chem., 23, 43-48, (1999)
[7]	Entringer, R.C.; Jackson, D.E.; Snyder, D.A., Distance in graphs, Czechoslovak math. J., 26, 283-296, (1976) · Zbl 0329.05112
[8]	Gutman, I.; Polansky, O.E., Mathematical concepts in organic chemistry, (1986), Springer Berlin · Zbl 0657.92024
[9]	Gutman, I.; Chen, J.C.; Yeh, Yeong-Nan, On the sum of all distances in graphs, Tamkang J. math., 25, 83-86, (1993) · Zbl 0808.05048
[10]	Gutman, I.; Lee, S.L.; Luo, Y.L.; Yeh, Yeong-Nan, Recent results in the theory of the Wiener number, Indian J. chem., 32A, 651-661, (1993)
[11]	Gutman, I.; Yeh, Y., On the sum of all distances in composite graphs, Discrete math., 135, 359-365, (1994) · Zbl 0814.05033
[12]	Plesnik, J., On the sum of distances in a graph or digraph, J. graph theory, 8, 1-21, (1984) · Zbl 0552.05048
[13]	Yan, Weigen; Yang, Bo-Yin; Yeh, Yeong-Nan, The behavior of Wiener indices and polynomials of graphs under five graph decorations, Appl. math. lett., 20, 290-295, (2007) · Zbl 1118.05026