S. Morteza Mirafzal
Abstract
Let $n >3$ and $ 0 1, $ if $n \neq 2k+1$, then the line graph of the graph $ {Q_n}(k,k+1) $ is a vertex-transitive non Cayley graph. Also, we show that the line graph of the graph $ {Q_n}(1,2) $ is a Cayley graph if and only if $ n$ is a power of a prime $p$.
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Let $n >3$ and $ 0 1, $ if $n \neq 2k+1$, then the line graph of the graph $ {Q_n}(k,k+1) $ is a vertex-transitive non Cayley graph. Also, we show that the line graph of the graph $ {Q_n}(1,2) $ is a Cayley graph if and only if $ n$ is a power of a prime $p$.
Key concepts: Vertex-transitive graph, Cayley graph, Combinatorics, Line graph, Mathematics, Symmetric graph, Graph, Petersen graph