On the radius of neighborhood graphs. Issue 5 (11th August 2016)

• Record Type: Journal Article
• Authors: Mukwembi, Simon; Vetrík, Tomáš
• Is Part Of: Quaestiones mathematicae. Volume 39:Issue 5(2016)
• Page Start: 577
• Page End: 585
• Publication Date: 2016-08-11
• Subjects: 05C12 -- 05C35; Neighborhood graph -- k-step graph -- radius; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2015.1113211
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: The k -step graph of a graph G has the same vertex set as G and two vertices are adjacent in if and only if there exists a path of length k connecting them in G . The graph is called the neighborhood graph of G . We present results on the connectivity and the radius of k -step graphs, especially on the radius of neighborhood graphs. For connected graphs we state bounds on the radius of in terms of the radius of G and we show that the bounds are sharp. For disconnected graphs, we give exact values of the radii of components of .