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math.CO2008
Maximum Multiplicity of a Root of the Matching Polynomial of a Tree and Minimum Path Cover
Cheng Yeaw Ku, K. B. Wong
We give a necessary and sufficient condition for the maximum multiplicity of a root of the matching polynomial of a tree to be equal to the minimum number of vertex disjoint paths…
math.CO2008
An Analogue of the Gallai-Edmonds Structure Theorem for Nonzero Roots of the Matching Polynomial
Cheng Yeaw Ku, William Chen
Godsil observed the simple fact that the multiplicity of 0 as a root of the matching polynomial of a graph coincides with the classical notion of deficiency. From this fact he aske…
math.CO2008
Eigenvalues of the Derangement Graph
Cheng Yeaw Ku, David B. Wales
We consider the Cayley graph on the symmetric group Sn generated by derangements. It is well known that the eigenvalues of this grpah are indexed by partitions of n. We investigate…