Year: 2023
Type: article
Abstract: The Kn\"odel graph $W_{\Delta,n}$ is a $\Delta$-regular bipartition graph on $n\ge 2^{\Delta}$ vertices and $n$ is an even integer. The vertices of $W_{\Delta,n}$ are the pairs $(i,j)$ with $i=1,2$ and $0\le j\le n/2-1$. For every $j$, $0\le j\le n/2-1$, there is an edge between vertex $(1, j)$ and every vertex $(2,(j+2^k-1) \mod (n/2))$, for $k=0,1,\cdots,\Delta-1$. In this paper we obtain some formulas for evaluating the distance of vertices of the Kn\"odel graph and by them, we provide the formula $diam(W_{\Delta,n})=1+\lceil\frac{n-2}{2^{\Delta}-2}\rceil$ for the diameter of $W_{\Delta,n}$, where $n\ge (2\Delta-5)(2^{\Delta}-2)+4$. Comment: 16 pages, 1 table, 2 figures
Source: Fundamenta Informaticae
DOI: 10.46298/fi.12318
Authors: Seyed Reza Musawi, Esameil Nazari Kiashi
Institution: University of Shahrood
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4386345967