%0 Journal Article
%T On the new extension of distance-balanced graphs
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Faghani, Morteza
%A Pourhadi, Ehsan
%A Kharazi, Hassan
%D 2016
%\ 12/01/2016
%V 5
%N 4
%P 21-34
%! On the new extension of distance-balanced graphs
%K $n$-distance-balanced property
%K lexicographic product
%K total distance
%R 10.22108/toc.2016.15048
%X 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.
%U http://toc.ui.ac.ir/article_15048_3968109258ac5aaddf5a16c03fc677d5.pdf