2 papers
math.CO2025
On the multiplicity of matching polynomial roots and -critical graphs
Leyou Xu
The matching polynomial of a graph encodes rich combinatorial information through its roots. We determine the maximum multiplicity of a non-zero matching polynomial root and charac…
math.CO2025
Proof of a conjecture on eigenvalues of transposition graph
Cheng Yeaw Ku, Leyou Xu
The transposition graph is the Cayley graph on the symmetric group generated by the set of all transpositions. In this paper, we show that each integer i…