Some Remarks on the 2-Distance-Balanced Graphs - Kharazi, Hassan; Alaeiyan, Mehdi (Communications in Mathematics and Applications, 2017)
The aim of this paper is to investigate the notion of 2-distance-balanced graphs as a generalized form of distance-balanced graphs. Furthermore, we introduce a subclass of such graphs so-called strongly 2-distance-balanced graphs and present some related results based on Cartesian and lexicographic products of two graphs.