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Let X 1⁄4 CayðG; SÞ be a 2-valent connected Cayley digraph of a regular p-group G and let GR be the right regular representation of G. It is proved that if GR is not normal in Aut(X ) then X ffi ~C2n 1⁄22K1 with n > 1, AutðX Þ ffi Z2wrZ2n , and either G 1⁄4 Z2nþ1 1⁄4 hai and S 1⁄4 fa; a2nþ1g, or G 1⁄4 Z2n Z2 1⁄4 hai hbi and S 1⁄4 fa; abg.
The global positioning system (GPS) provides accurate positioning and timing information that is useful in many applications. In particular, portable consumer GPS applications require cheap compact low-power receivers. This 115mW receiver, implemented in an analog 0.5μm CMOS technology, comprises the entire radio-frequency (RF) and analog sections in(More)
A graph is half-arc-transitive if its automorphism group acts transitively on its vertex set, edge set, but not arc set. Let p and q be primes. It is known that no tetravalent half-arc-transitive graphs of order 2p2 exist and a tetravalent half-arctransitive graph of order 4p must be non-Cayley; such a non-Cayley graph exists if and only if p − 1 is(More)
A graph is 1-arc-regular if its full automorphism group acts regularly on the set of its arcs. In this paper, we investigate 1-arc-regular graphs of prime valency, especially of valency 3. First, we prove that if G is a soluble group then a (G, 1)-arc-regular graph must be a Cayley graph of a subgroup of G . Next we consider trivalent Cayley graphs of a(More)