Index
alternating sign matrix (ASM), 79
pattern, 83
bipartite graph, 1, 78
complete, 1
eigenvalues, 15
left vertex, 1
right vertex, 1
diagonal product, 49, 61–64
signed, 49
digraph, 49, 60, 87
acyclic, 88
cycle, 51
eigenvalues, 87
nonnegative, 88
positive, 88
strongly connected, 60
weighted, 49
dimer problem, 53
equal union property, 54
graph, 13
adjacency matrix, 13
weighted, 33
algebraic connectivity, 22
alternating sign, 85
biclique, 27
biclique partition number, 27
lower bound, 29
chromatic number, 16
lower bound, 18
upperbound, 18
clique, 17, 27
Colin de Verdi` ere number, 33–35
complete graph, 35
linklessly embeddable, 36
outerplanar, 36
path, 36
planar, 36, 37
complement, 17, 35
connected, 14
diameter, 15
edge connectivity, 22
eigenvalues, 13, 14
independence number, 16
Laplacian matrix, 21
minor, 35
forbidden, 35
minor-closed, 35
proper, 35
multicolored, 30
spanning forest, 30
spanning tree, 30
planar, 35
regular, 17
Smith, 20
spanning tree
number, 21
vertex connectivity, 22
interchange, 44
generalization, 47
graph, 44
L-matrix, 53
Laplacian matrix, 21
lemniscate, 62
majorization, 42, 45, 69, 73
Muirhead’s lemma, 45
matrix
absolute value, 61
alternating sign, 79
conjecture, 80
ASM, 79
biadjacency, 39
classes, 39, 45, 69, 85
co-rank, 34
determinant, 21, 49
diagonally dominant, 59, 63
95
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