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arXiv · 1907.06752

Independence numbers of Johnson-type graphs

Danila Cherkashin·Sergei Kiselev
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Abstract

We consider a family of distance graphs in $\mathbb{R}^n$ and find its independent numbers in some cases. Define graph $J_{\pm}(n,k,t)$ in the following way: the vertex set consists of all vectors from $\{-1,0,1\}^n$ with $k$ nonzero coordinates; edges connect the pairs of vertices with scalar product $t$. We find the independence number of $J_{\pm}(n,k,t)$ for $n > n_0 (k,t)$ in the cases $t = 0$ and $t = -1$; these cases for $k = 3$ are solved completely. Also the independence number is found for negative odd $t$ and $n > n_0 (k,t)$.

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Danila Cherkashin, Sergei Kiselev. 2022-10-05. Independence numbers of Johnson-type graphs. https://arxiv.org/abs/1907.06752

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