Diameter of General Knödel Graphs

Article type: Research Article

Authors: Musawi, Seyed Reza^{a; *} | Nazari, Esmaeil^b

Affiliations: [a] Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 36199-95161, Shahrood, Iran. r_musawi@shahroodut.ac.ir | [b] Department of Mathematics, Tafresh University, Tafresh, Iran. nazari.esmaeil@gmail.com

Correspondence: [*] Address for correspondence: Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 36199-95161, Shahrood, Iran

Abstract: The Knödel graph WΔ,n is a Δ-regular bipartite graph on n ≥ 2Δ vertices where n is an even integer. In this paper We obtain some results about the distances of two vertices in the Knödel graphs and by them, we prove that diam(WΔ,n)=1+⌈n−22Δ−2⌉, where Δ ≥ 2 and n ≥ (2Δ – 5)(2Δ – 2) + 4.

Keywords: Knödel Graph, distance, diameter

DOI: 10.3233/FI-222165

Journal: Fundamenta Informaticae, vol. 190, no. 1, pp. 47-62, 2022