A new achievement from reviewing some of the content about the edge-distance-balanced property of the generalized Petersen graphs \(GP (4i + 7, 2)\). (English) Zbl 1485.05042
This article is on edge distance-balanced graphs, a concept related to distance balancedness in graphs. A graph \(G\) is said to be edge-distance-balanced if for any edge \(uv\) of \(G\), the number of edges closer to \(u\) than to \(v\) is equal to the number of edges closer to \(v\) than to \(u\). The main contribution of this article is that generalized Petersen graphs \(GP(4i + 7, 2)\), for \(i\geq 3\) are not edge distance balanced and that they are not strongly distance balanced. This article may be of interest to metric graph theoreticians.
Reviewer: Manoj Changat (Trivandrum)
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