论文信息 - On tournament matrices

On tournament matrices

Abstract Let T be a tournament of order n with adjacency matrix M. We find several conditions that are equivalent to M being singular. A correlation between the number of 3-cycles in T and the rank of M is established. It is shown that asymptotically at least 1 2 of the tournament matrices are nonsingular. We also derive bounds on the spectral radius of tournament matrices with a given row-sum vector.

Bryan L. Shader | B. Shader

[1] R. Rado,et al. Theorems on Linear Combinatorial Topology and General Measure , 1943 .

[2] J. Moon. Topics on tournaments , 1968 .

[3] Ronald L. Graham,et al. On the addressing problem for loop switching , 1971 .

[4] M. Kendall,et al. ON THE METHOD OF PAIRED COMPARISONS , 1940 .

[5] G. W. Peck,et al. A new proof of a theorem of Graham and Pollak , 1984, Discret. Math..

[6] P. Moran. On the method of paired comparisons. , 1947, Biometrika.

[7] J. Maybee,et al. Tournament matrices and their generalizations, I. , 1990 .

[8] J. Gillis,et al. Matrix Iterative Analysis , 1961 .

[9] A. Brauer,et al. On the characteristic roots of tournament matrices , 1968 .

[10] D. G. Hoffman,et al. Impossibility of Decomposing the Complete Graph on n Points into n-1 Isomorphic Complete Bipartite Graphs , 1989, SIAM J. Discret. Math..

[11] R. Graham,et al. On embedding graphs in squashed cubes , 1972 .

[12] H. Landau. On dominance relations and the structure of animal societies: III The condition for a score structure , 1953 .

[13] L. Beineke,et al. Selected Topics in Graph Theory 2 , 1985 .