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We show that the eccentricity matrix of a chain graph has a gap interval, i.e., an interval with no eccentricity eigenvalues in it. Our considerations are grounded on the row equivalence of two matrices: the characteristic matrix of the quotient matrix of the eccentricity matrix of a chain graph and a particular polynomial matrix whose underlying graph is a cycle.

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Gap Intervals of Eccentricity Matrices of Chain Graphs

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  • 发表日期：

    2025年

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  • Abdullah Alazemi,
  • Milica Anđelić

摘要

We show that the eccentricity matrix of a chain graph has a gap interval, i.e., an interval with no eccentricity eigenvalues in it. Our considerations are grounded on the row equivalence of two matrices: the characteristic matrix of the quotient matrix of the eccentricity matrix of a chain graph and a particular polynomial matrix whose underlying graph is a cycle.