On the new extension of distance-balanced graphs
نویسندگان
1 Department of Mathematics, Payame Noor University, P.O.Box 9395-3697, Tehran, Iran
2 School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran
3 Department of Mathematics and Statistics, Imam Hossein University, Tehran, Iran
doi
10.22108/toc.2016.15048چکیده
In this paper, we initially introduce the concept of $n$-distance-balanced property which is considered as the generalized concept of distance-balanced property. In our consideration, we also define the new concept locally regularity in order to find a connection between $n$-distance-balanced graphs and their lexicographic product. Furthermore, we include a characteristic method which is practicable and can be used to classify all graphs with $i$-distance-balanced properties for $ i=2,3 $ which is also relevant to the concept of total distance. Moreover, we conclude a connection between distance-balanced and 2-distance-balanced graphs.
