Steiner Wiener Index of Certain Windmill Graphs.
DOI:
https://doi.org/10.21271/ZJPAS.35.5.5Keywords:
Steiner distance, Steiner Wiener index, windmill graphsAbstract
For a connected graph of order and a non-empty subset , the - Steiner distance of is defined to be the smallest size among all connected subgraphs whose vertex sets contain . In this paper, we obtain the Hosoya polynomials of Steiner -distance of some windmill graphs. Moreover, the Steiner Wiener indices of certain windmill graphs are also obtained.
References
Ali, A.A. and Saeed, W.A; (2006), “Wiener polynomials of Steiner distance of graphs”, J. of Applied Sciences, 8(2): 64-71.
Ali A. , Ravindra B. B. and Shivani G.;(2022). Steiner distance matrix of caterpillar graphs. De Gruyter, 10(1): 267-284.
Babu, A. and Baskar, J. B.; (2019). Steiner Reciprocal Degree Distance Index. Appl. Math. Inf. Sci., 13(S1): 149-155.
Buckly, F. and Harary, F.;(1990), Distance in Graphs, Addison-Wesley, Redwood, California.
Chartrand, G. and Lesniak, L.; (1986), Graphs and Digraphs, 2nd ed., Wadsworth and Brooks/ Cole, California.
Chartrand G., Oellermann O.R. ,Tian, S. L. and Zou, H.B.; (1989). Steiner distance in graphs, Časopis pro pěstování matematiky, 114: 399–410.
Danklemann, P., Oellermann, O. R., and Swart, H.C.; (1996). The average Steiner distance of a graph. J. Graph Theory, 22(1):15-22.
Gary, M. R. and Johson, D. S., (1979). Computers and Interactability: A Guide to the Theory of NP-Completeness. Freeman and Company, New York.
Herish, O.A.;(2009). Hosoya Polynomials of Steiner Distance of the Sequential Join of Graphs. Raf. J. of Comp. & Math’s. , 6(2): 85-95.
Izudin, R., Yaping, M., Zhao W. and Boris F.; (2020). Steiner degree distance indices: Chemical applicability and bounds. International Journal of Quantum Chemistry, 120(12):1-9.
Patrick, A. and Edy T. B; (2022). Bounds on the Steiner radius of a graph. Discrete Mathematics, Algorithms and Applications, 14(2): 1-9.
V. R. Kulli, Praveen Jakkannavar and B. Basavanagoud;(2019). Computation of leap hyper-Zagreb indices of certain windmill graphs. International Journal of Scientific Research in Mathematical and Statistical Sciences, 6(2): 75-79
Xueliang, L. , Yaping, M. and Ivan, G.; (2016). The Steiner Wiener Index of a Graph. Discussiones Mathematicae Graph Theory, 36: 455–465.
Yaping, M., Boris, F.; (2021). Steiner distance in chemical graph theory-A survey, MATCH Communication in Mathematical and in Computer Chemistry 86(2): 211-288.
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Copyright (c) 2023 Herish Omer Abdullah
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