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- W4287118081 abstract "A $k$-regular graph is called a divisible design graph (DDG for short) if its vertex set can be partitioned into $m$ classes of size $n$, such that two distinct vertices from the same class have exactly $lambda_1$ common neighbors, and two vertices from different classes have exactly $lambda_2$ common neighbors. $4times n$-lattice graph is the line graph of $K_{4,n}$. This graph is a DDG with parameters $(4n,n+2,n-2,2,4,n)$. In the paper we consider DDGs with these parameters. We prove that if $n$ is odd then such graph can only be a $4times n$-lattice graph. If $n$ is even we characterise all DDGs with such parameters. Moreover, we characterise all DDGs with parameters $(4n,3n-2,3n-6,2n-2,4,n)$ which are related to $4times n$-lattice graphs." @default.
- W4287118081 created "2022-07-25" @default.
- W4287118081 creator A5059804919 @default.
- W4287118081 date "2021-06-16" @default.
- W4287118081 modified "2023-09-26" @default.
- W4287118081 title "Divisible design graphs with parameters $(4n,n+2,n-2,2,4,n)$ and $(4n,3n-2,3n-6,2n-2,4,n)$" @default.
- W4287118081 doi "https://doi.org/10.48550/arxiv.2106.08677" @default.
- W4287118081 hasPublicationYear "2021" @default.
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