New families of graphs determined by their generalized spectrum
Fenjin Liu, Johannes Siemons, Wei Wang
TL;DR
This paper introduces new infinite families of graphs uniquely identified by their generalized spectrum, using novel formulas for the walk matrix determinant that satisfy specific divisibility properties.
Contribution
It presents a new construction method for graphs determined by their generalized spectrum based on walk matrix determinant formulas and divisibility conditions.
Findings
Constructed infinite families of graphs determined by their generalized spectrum
Derived new formulas for the determinant of the walk matrix
Identified divisibility properties of walk matrix determinants
Abstract
We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. The graphs constructed here all satisfy a lower divisibility for the determinant of their walk matrix.
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Taxonomy
TopicsGraph theory and applications · graph theory and CDMA systems · Matrix Theory and Algorithms