Paper Title:

Generalized k-distance-balanced Graphs

Author(s):

Amir Hosseini and Mehdi Alaeiyan

Department of mathematics, Karaj Branch,
Islamic Azad university, Karaj,
Iran.
E-mail: amir.hosseini@kiau.ac.ir, hosseini.sam.52@gmail.com

Department of Mathematics,
Iran University of Science and Technology, Tehran,
Iran.
E-mail: alaeiyan@iust.ac.ir

Abstract:

A nonempty graph Γ is called generalized k-distance-balanced, whenever every edge ab has the following property: the number of vertices closer to a than to b, k^, times of vertices closer to b than to a, or conversely, k∈ N .In this paper we determine some families of graphs that have this property, as well as to prove some other result regarding these graphs.

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