Abstract.
Distance-balanced graphs are introduced as graphs in which every edge uv has the following property The number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. The new concept is connected with symmetry conditions in graphs and local operations on graphs are studied with respect to it. Distance-balanced Cartesian and lexicographic products of graphs are also characterized. Several open problems are posed along the way.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Received August 31, 2005
Rights and permissions
About this article
Cite this article
Jerebic, J., Klavžar, S. & Rall, D.F. Distance-Balanced Graphs. Ann. Comb. 12, 71–79 (2008). https://doi.org/10.1007/s00026-008-0337-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00026-008-0337-2