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  • Connectivity, domination and perfect codes in product graphs : doctoral thesis
    Špacapan, Simon
    We consider several problems on the Cartesian, the direct and the strong product of graphs. We determine vertex connectivity of the Cartesian product and characterize minimum separating sets in the ... strong product of graphs. Edge connectivity for the strong product of graphs is determined as well. For the direct product of graphs we give sharp lower and upper bounds for the edge connectivity. We give necessary and sufficient conditions for existence of perfect codes in direct products of cycles and almost completely charactarize the existence of perfect codes in these graphs. Explicit construction of perfect codes in direct products of cycles is also provided. Broadcast domination is considered on all three graph products, where upper and lower bounds are obtained. Some exact values for the broadcast domination number of some classes of graphs are obtained. Optimal local structures in Cartesian products of cycles and tilings in a four-dimensional space (which are related to perfect Lee codes) are considered. Nonexistance theorems for optimal local structures and tilings are given. Total domination is also studied on direct products, where some bounds on this graph invariant are obtained.
    Type of material - dissertation ; adult, serious
    Publication and manufacture - [Maribor : S. Špacapan], 2007
    Language - english
    COBISS.SI-ID - 232631552

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