Integral quartic Cayley graphs on Abelian groups.
Abdollahi, A., Vatandoost, E. (2011)
The Electronic Journal of Combinatorics [electronic only]
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Integral quartic Cayley graphs on Abelian groups.
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Every connected graph G with radius r(G) and independence number α(G) obeys α(G) ≥ r(G). Recently the graphs for which equality holds have been classified. Here we investigate the members of this class that are Cartesian products. We show that for non-trivial graphs G and H, α(G ☐ H) = r(G ☐ H) if and only if one factor is a complete graph on two vertices, and the other is a nontrivial complete graph. We also prove a new (polynomial computable) lower bound α(G ☐ H) ≥ 2r(G)r(H)...