TITLE:
Some Results on Generalized Degree Distance
AUTHORS:
Asma Hamzeh, Ali Iranmanesh, Samaneh Hossein-Zadeh
KEYWORDS:
Generalized Degree Distance; Cartesian Product; Join; Symmetric Difference; Composition; Disjunction
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.3 No.3,
July
12,
2013
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 modified
generalized degree distance. These polynomials are related to Wiener-type invariant polynomial of graphs.