Is the corona of a cycle C_n and the empty graph \overline(K_m) a prime graph for all n and m?

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Norman Bradley Fox

Yes, that is the paper I are referring to. I have gained access to it since I asked the question and see that they did in fact show this corona graph is prime for all m and n.

Maged Z. Youssef

Yes, the graph is prime. It is can be shown easily. There is a conjecture due to Seoud and Youssef in 1999 (in Congrussus Numerantium ) states that every unicyclic graph is prime