Automorphisms of $\omega$-octahedral graphs.
J. C. E. Dekker · Notre Dame Journal of Formal Logic · 1982
This paper is closely related to [2] which deals with automorphisms of the co-graph Q^ associated with the co-cube Q N and [3] which deals with the co-graph Oc^ associated with the co-octahedron Oc^.We use the notations, terminology, and results of [2].The propositions of [2] are referred to as Al.l, A1.2, . .., A2.1, A2.2, . . .etc., those of [3] as Bl.l, B1.2, . .., B2.1,B2.2, . ..etc.For n > 1 the ^-octahedral graph is defined as the complete rc-partite graph K(2, . .., 2) with two vertices in each of its partite sets ([4], p. 69).Let Oc n have M = (0,. .., 2n -1) as set of vertices and ((0,1), . .., (In -2, 2w -1)) as class of its partite sets.Define / as the permutation of JJL which for 0 2.An involution without fixed points (abbreviated: iwfp) of a set JU is a permutation / of /x such that f 2 = / M and fix) =£ x, for x e /x.The iwfp / of /x is an co-iwfp, if it has a partial recursive one-to-one extension.With every iwfp / of JU we associate a graph Gf = .The standard cooctahedral graph Oc v associated with the set v is the co-graph Gf = {JJL U , 0 V ),