On isomorphic, nonisomorphic and the number of tournaments from three tournament construction algorithms
A tournament T of order n is a digraph V(T), A(T) with vertex-set V(T)=&1,2,...,n such that for every pair of distinct vertices i and j in V(T), (i,j) element A(T) or (j,i) element A(T) but not both. The score Si of a vertex i element V(T) is the number of arcs (i,j) element A(T). In this thesis...
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| Format: | text |
| Language: | English |
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Animo Repository
1999
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_masteral/2026 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | A tournament T of order n is a digraph V(T), A(T) with vertex-set V(T)=&1,2,...,n such that for every pair of distinct vertices i and j in V(T), (i,j) element A(T) or (j,i) element A(T) but not both. The score Si of a vertex i element V(T) is the number of arcs (i,j) element A(T). In this thesis, it is assumed that the vertices of T are labeled in such a way that S1 is less than or equal to S2 less than or equal to...less than or equal to Sn. The nondecreasing sequence Si1 less than or equal to i less than or equal to n = s1,S2,...,Sn is called the score sequence of T. The sequence di 1 less than or equal to i less than or equal to n=d1,d2...,dn where di = si-i+1 is called its deviation sequence.This study gives sufficient conditions in isomorphic and nonisomorphic tournaments constructed from the three tournament construction algorithms of Gervacio in [6,7]. The number of tournaments with a specified score sequence constructed from each algorithm are also determined. |
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