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Distance-Balanced Graphs |
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| Authors: | Janja Jerebic Sandi Klavžar Douglas F. Rall |
| Affiliation: | (1) Department of Mathematics and Computer Science FNM, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia;(2) Department of Mathematics, Furman University, Greenville, SC 29613, USA |
| 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. Received August 31, 2005 |
| Keywords: | KeywordHeading" >: graph distance distance-balanced graphs graph products connectivity |
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