A root graph that is locally the line graph of the Petersen graph
The authors construct a root graph on \(192\) vertices that is locally the line graph of the Petersen graph and they show that this graph is the unique root graph with \(\mu = 2\) that is locally the line graph of the Petersen graph (\(\mu = 2\) means that every two vertices at distance two have precisely two common neighbours). Moreover, a new distance-regular graph on \(96\) vertices (with intersection array \(\{15,10,1;1,2,15\}\) and automorphism group \(2^4 \text{Sym}(6)\)) and several new strongly regular graphs (with parameters \((v,k,\lambda,\mu) = (96,20,4,4)\) and \((96,19,2,4)\)) and square \(2\)-\((96,20,4)\) designs are constructed.
scientific article; zbMATH DE number 1896019