Sharif Digital Repository

In this thesis which is an extensive expository and survey, we study concepts like irreducible, primitive, regular and almost regularournaments. We study and show the proof of some graph theoretical properties of tournaments such as being pancyclic, vertex or arc-pancyclic, and a lower bound on the number of cycles of each length in irreducible tournaments. Spectral properties and the Perron eigenvalue of tournament matrices are also extensively discussed.The ranks of tournament matrices over different algebraic fields, is another subjectthat is covered. We have written computer programs to study the distribution of the rank of tournament matrices over Z2.With a little more work,one might... 

In 1953, Landau expressed the conditions for the existence of tournaments with a prescribed score vector R. Eleven years later, Ryser proposed an algorithm for constructing the tournament matrix with score vector R and showed that any two tournaments with the same score vector can be obtained from one another by a sequence of 3-cycle switches. Last year (2014) Brualdi and Fristcher explained in an article, similar to this process, the existence of, algorithm and switches for loopy tournament and Hankel tournament and similar structure skew-Hankel tournament. This paper is discussed in a chapter of this thesis. In 1991, De Caen found a lower bound for the real rank of a tournament matrix....