D-Levels locally homogeneous graphs. (3rd September 2015)

• Record Type: Journal Article
• Authors: Al-Addasi, Salah
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 18:Number 5(2015)
• Page Start: 663
• Page End: 672
• Publication Date: 2015-09-03
• Subjects: Diametrical graph -- S-Graph -- Locally homogeneous graph -- D-Levels locally homogeneous graph -- k-Levels locally homogeneous graph -- Vertex-transitive graph; 05C12 -- 05C75 -- 05C99; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2015.1032623
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: This article introduces the concept of a D -levels locally homogeneous graph which forms a special type of self-centered graphs. Some results relating D -levels locally homogeneous graphs to diametrical graphs (which are also self-centered) are obtained. Diametrical graphs of small order (≤ 8) are shown to be D -levels locally homogeneous. When the diameter is 2, it is shown that the concept of a D -levels locally homogeneous graph and that of a diametrical graph coincide. Bipartite diametrical graphs of diameter 3 and regular S -graphs of diameter 4 are characterized as D -levels locally homogeneous graphs. We also prove that the vertex-transitive graphs are precisely the totally D -levels locally homogeneous graphs.