A new achievement from reviewing some of the content about the edge-distance-balanced property of the generalized Petersen graphs GP(4i + 7, 2). (17th February 2021)

• Record Type: Journal Article
• Authors: Ezadi, Mahboubeh
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 24:Number 2(2021)
• Page Start: 391
• Page End: 399
• Publication Date: 2021-02-17
• Subjects: 05C38 -- 05C12; Edge-distance-balanced graph -- Generalized Petersen graph -- Distance-balanced graph; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2021.1905746
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: In this paper, we initially introduce the concept of edge-distance-balanced property which is considered as the generalized concept of distance-balanced property. In our consideration, we will discover some interesting properties of generalized Petersen graphs that called edge distance-balanced graphs. We also define a connection between edge-distance-balanced graphs and distance-balanced graphs. Furthermore, 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 . It will be concluded that for any round number i ≥ 3, the generalized Petersen graph GP (4 i + 7, 2) is not edge-distance-balanced.