## Palanivel Subramania Nadar Paulraja ; S Sampath Kumar - Edge Disjoint Hamilton Cycles in Knödel Graphs

dmtcs:2148 - Discrete Mathematics & Theoretical Computer Science, July 22, 2016, Vol. 17 no. 3 - https://doi.org/10.46298/dmtcs.2148
Edge Disjoint Hamilton Cycles in Knödel Graphs

Authors: Palanivel Subramania Nadar Paulraja 1; S Sampath Kumar 2

• 1 Department of Mathematics, Kalasalingam University
• 2 Department of Mathematics, SSN College of Engineering

The vertices of the Knödel graph $W_{\Delta, n}$ on $n \geq 2$ vertices, $n$ even, and of maximum degree $\Delta, 1 \leq \Delta \leq \lfloor log_2(n) \rfloor$, are the pairs $(i,j)$ with $i=1,2$ and $0 \leq j \leq \frac{n}{2} -1$. For $0 \leq j \leq \frac{n}{2} -1$, there is an edge between vertex $(1,j)$ and every vertex $(2,j + 2^k - 1 (mod \frac{n}{2}))$, for $k=0,1,2, \ldots , \Delta -1$. Existence of a Hamilton cycle decomposition of $W_{k, 2k}, k \geq 6$ is not yet known, see Discrete Appl. Math. 137 (2004) 173-195. In this paper, it is shown that the $k$-regular Knödel graph $W_{k,2k}, k \geq 6$ has $\lfloor \frac{k}{2} \rfloor - 1$ edge disjoint Hamilton cycles.

Volume: Vol. 17 no. 3
Section: Graph Theory
Published on: July 22, 2016
Submitted on: July 31, 2014
Keywords: Bieulerian Graph, Tensor Product,Knödel Graphs, Hamilton Cycle Decomposition,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]