The trees for which maximum multiplicity implies the simplicity of other eigenvalues

Johnson, Charles R.Saiago, Carlos Manuel2019-01-232019-01-232006-12-060012-365XPURE: 354119PURE UUID: 7eef470d-13b3-4d3a-81c4-60be6035cabfresearchoutputwizard: 11750WOS: 000242276000017Scopus: 33750975068ORCID: /0000-0001-9843-3821/work/53864377http://hdl.handle.net/10362/58384Among those real symmetric matrices whose graph is a given tree $T$, the maximum multiplicity is known to be the path cover number of $T$. An explicit characterization is given for those trees for which whenever the maximum multiplicity is attained, all other multiplicities are $1$.6189296engReal symmetric matricesEigenvaluesMultiplicitiesMaximum multiplicityTreesNIM treesVertex degreesThe trees for which maximum multiplicity implies the simplicity of other eigenvaluesjournal article10.1016/j.disc.2005.04.026