Semenyuta M. The investigation of graph decompositions and graph labelings

The dissertation studies the decompositions and labelings of graphs. The existence of cyclic (K21,G)-decompositions for each connected (7,10)-graphs G is established. The investigation of the cyclic pentagonal decompositions of the graph Kn for n?1(mod10), prismatic and periwinklic decompositions of the graph K19 are presented. A method of the construction of the basic components of such decompositions, and lists of different cyclic (K11, C5)- and (К21,С5)-decompositions is founded. The number of nonisomorphic 1-factorisation of the graph Q5 is found, the uniqueness of the square 1-factorisation of the graph Qn is proven for every n. It is proved that the automorphism group of the square 1-factorisation of Qn coincides with the automorphism group of the graph. The antimagicity of certain classes of graphs is investigate.