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Some Results on Generalized Degree Distance
Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
- 1 Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
- 2 Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
- 3 Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
Open Journal of Discrete Mathematics·Volume 03 (2013)·Pages 143–150·Published 2 July 2013·DOI10.4236/ojdm.2013.33026
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Abstract
In [1], Hamzeh, Iranmanesh and Hossein-Zadeh and M. V. Diudea recently introduced the generalized degree distance of graphs. In this paper , we present explicit formulas for this new graph invariant of the Cartesian product, composition, join, disjunction and symmetric difference of graphs and introduce generalized and modified generalized degree distance polynomials of graphs, such that their first derivatives at x = 1 are respectively, equal to the generalized degree distance and the modi fied generalized degree distance. These polynomials are related to Wiener-type invariant polynomial of graphs.
KeywordsGeneralized Degree DistanceCartesian ProductJoinSymmetric DifferenceCompositionDisjunction
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