The Score Sets of Digraphs and related results

Abstract

In chapter 1 we mention some basic definitions which have been used in newlinethe thesis In chapter 2 we study score sequences of tournaments bipartite tournaments 3 partite tournaments k partite tournaments and score sets of tournaments and bipartite tournaments We obtain a result on score sets of tournaments and determine the number o f bipartite score sequences of order 2*n Further we prove that every set of non negative integers except 0 and newline0 1 is a score set of some 3 partite tournament and every set of non negative newlineintegers is a score set o f some k partite tournament for every tgtkgt2 In chapter 3 we give a brief review of the score sequences of oriented graphs In chapter 4 we study score sequences of oriented bipartite graphs In chapter 5 we give a brief review of the score sequences of oriented 3 partite graphs and oriented k partite graphs and obtain new results on score sets of such oriented graphs In chapter 6 we study one newlinemore class of digraphs known as 2 digraphs and present the mark structure of such digraphs We obtain stronger inequalities for marks in 2 digraphs Further newlinesome results on mark sets of 2 digraphs are also obtained