الفهرس يوجد فقط 14 صفحة متاحة للعرض العام
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المستخلص
In this thesis, we investigate and study a class of highly regular graph d< positions. Graph decompositions have been studied since the 19th century. The investigation is originated by various combinatorial problems, the best, known amoi them are Kirkman’s problems of 15 strolling schoolgirls and Euler’s problems of : army oilicers. Many combinatorial and algebraic structures are linked to these o jects. For an overview of the subject, the reader may refer to the book of Bos; [14]. The vast results in this area are summarized in the CR.C Handbook of C’oi binatorial Designs [4]. This thesis contributes to the study of special class of gra1 decompositions, called orthogonal double; cover (ODC’) of complete bipartite grap and complete graphs.
Orthogonal double cover (ODC} of KHtH is a collection Q of 2n graphs (each gra labeled with a vertex) such that each edge of Klltll occurs in exactly two of the; gra[ and any two graphs Gx, Gy have one edge in common if and only if x and // are je>h by an edge in Kn,n- If all graphs in the collection Q are isomorphic to a graph G. tl we call Q an (ODC) of Kn
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existence of the orthogonal double cover of the complete; bipartite graph A”; and ejf the complete graph Kn by G, for certain, infinite classes of C.
In chapter 1, the basic definitions and notations are: preseuited. and the bad information about orthogonality are; given also.