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  • Finite graphs of valency 4 and girth 4 admitting half-transitive group actions
    Marušič, Dragan ; Nedela, Roman
    Finite graphs of valency 4 and girth 4 admitting 1/2-transitive group actions, that is vertex- and edge- but not arc-transitive group actions, are investigated. A graph is said to be 1/2-transitive ... if its automorphism group acts 1/2-transitively. There is a natural (balanced) orientation of the edge set of a 1/2-transitive graph induced and preserving by its automorphism group. Among others it is proved that in a finite 1/2-transitive graph of valency 4 and girth 4 the set of 4-cycles decomposes the edge set. Moreover, in this decomposition either every 4-cycle is alternating or every 4-cycle is transitive with respect to the above orientation. In the later case the vertex stabilizer is isomorphic to ▫$Z_2$▫.
    Vir: Preprint series. - ISSN 1318-4865 (Let. 35, št. 559, 1997, str. 1-21)
    Vrsta gradiva - članek, sestavni del
    Leto - 1997
    Jezik - angleški
    COBISS.SI-ID - 7327833

vir: Preprint series. - ISSN 1318-4865 (Let. 35, št. 559, 1997, str. 1-21)
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