Geometrical approach to Seidel's switching for strongly regular graphs - Mathematics > CombinatoricsReport as inadecuate




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Abstract: In this paper, we simplify the known switching theorem due to Bose andShrikhande as follows.Let $G=V,E$ be a primitive strongly regular graph with parameters$v,k,\lambda,\mu$.Let $SG,H$ be the graph from $G$ by switching with respect to a nonempty$H\subset V$.Suppose $v=2k-\theta 1$ where $\theta 1$ is the nontrivial positiveeigenvalue of the $0,1$ adjacency matrix of $G$. This strongly regular graphis associated with a regular two-graph.Then, $SG,H$ is a strongly regular graph with the same parameters if andonly if the subgraph induced by $H$ is $k-\frac{v-h}{2}$ regular. Moreover,$SG,H$ is a strognly regualr graph with the other parameters if and only ifthe subgraph induced by $H$ is $k-\mu$ regular and the size of $H$ is $v-2$. Weprove these theorems with the view point of the geometrical theory of thefinite set on the Euclidean unit sphere.



Author: Hiroshi Nozaki

Source: https://arxiv.org/







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