Graphs of unitary matrices

The support of a matrix M is the (0,1)-matrix with ij-th entry equal to 1 if the ij-th entry of M is non-zero, and equal to 0, otherwise. The digraph whose adjacency matrix is the support of M is said to be the digraph of M. This paper observes some structural properties of digraphs of unitary matrices.

[1]  Gregory Gutin,et al.  Digraphs - theory, algorithms and applications , 2002 .

[3]  Charles Delorme,et al.  Combinatorial Properties and the Complexity of a Max-cut Approximation , 1993, Eur. J. Comb..

[4]  Miroslav Fiedler,et al.  DOUBLY STOCHASTIC MATRICES AND OPTIMIZATION , 1988, Advances in Mathematical Optimization.

[5]  Daniel A. Spielman,et al.  Exponential algorithmic speedup by a quantum walk , 2002, STOC '03.

[6]  V. Klee,et al.  Combinatorial and graph-theoretical problems in linear algebra , 1993 .

[7]  Gregor Tanner,et al.  Unitary-stochastic matrix ensembles and spectral statistics , 2001, nlin/0104014.

[8]  Oriol Serra,et al.  Construction of k-arc transitive digraphs , 2001, Discret. Math..

[9]  R. Bhatia Matrix Analysis , 1996 .

[10]  W. T. Tutte The 1-factors of oriented graphs , 1953 .

[11]  H. Coxeter,et al.  Generators and relations for discrete groups , 1957 .

[12]  Simone Severini,et al.  Regular quantum graphs , 2004 .

[13]  Luisa Gargano,et al.  Capacities: From Information Theory to Extremal Set Theory , 1994, J. Comb. Theory, Ser. A.

[14]  Quantum graphs: a simple model for chaotic scattering , 2002, nlin/0207049.

[15]  L. Lovász Matching Theory (North-Holland mathematics studies) , 1986 .

[16]  G. Greco Capacities of graphs and 2-matchings , 1998, Discret. Math..

[17]  K. Birgitta Whaley,et al.  Quantum random-walk search algorithm , 2002, quant-ph/0210064.

[18]  Marie-Claude Heydemann,et al.  Cayley graphs and interconnection networks , 1997 .

[19]  Michael Aschbacher,et al.  Some applications of the first cohomology group , 1984 .

[20]  Frank Harary,et al.  Graph Theory , 2016 .

[21]  Gérard D. Cohen,et al.  Zero-error capacities and very different sequences , 1990 .

[22]  Simone Severini On the Digraph of a Unitary Matrix , 2003, SIAM J. Matrix Anal. Appl..

[23]  Paul D. Seymour,et al.  Nowhere-zero 6-flows , 1981, J. Comb. Theory, Ser. B.

[24]  James D. Louck,et al.  Doubly stochastic matrices in quantum mechanics , 1997 .

[25]  The possible numbers of zeros in a orthogonal matrix , 1999 .

[26]  Guo-Hui Zhang,et al.  Combinatorially orthogonal matrices and related graphs , 1998 .

[27]  Yik-Hoi Au-Yeung,et al.  Permutation matrices whose convex combinations are orthostochastic , 1991 .

[28]  Uzy Smilansky,et al.  Periodic Orbit Theory and Spectral Statistics for Quantum Graphs , 1998, chao-dyn/9812005.