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Creators/Authors contains: "Reinhart, Carolyn"

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  1. ; ; ; ; ; (, The Australasian journal of combinatorics)
    Accepted Manuscript Full Text Available
  2. ; ; ; (, The Electronic Journal of Linear Algebra)
    null (Ed.)
    A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the new distance matrix, with natural extensions to the distance Laplacian and distance signless Laplacian, in addition to the new adjacency matrix, with natural extensions to the Laplacian and signless Laplacian. Various sums of Kronecker products of nonnegative matrices are introduced to model the Cartesian and lexicographic products of digraphs. The Jordan canonical form is applied extensively to the analysis of spectra and eigenvectors. The analysis shows that Cartesian products provide a method for building infinite families of transmission regular digraphs with few distinct distance eigenvalues. 
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  3. ; ; ; ; ; ; (, The Electronic Journal of Linear Algebra)
    null (Ed.)
    The distance matrix $$\mathcal{D}(G)$$ of a graph $$G$$ is the matrix containing the pairwise distances between vertices, and the distance Laplacian matrix is $$\mathcal{D}^L (G)=T(G)-\mathcal{D} (G)$$, where $T(G)$ is the diagonal matrix of row sums of $$\mathcal{D}(G)$$. Several general methods are established for producing $$\mathcal{D}^L$$-cospectral graphs that can be used to construct infinite families. Examples are provided to show that various properties are not preserved by $$\mathcal{D}^L$$-cospectrality, including examples of $$\mathcal{D}^L$$-cospectral strongly regular and circulant graphs. It is established that the absolute values of coefficients of the distance Laplacian characteristic polynomial are decreasing, i.e., $$|\delta^L_{1}|\geq \cdots \geq |\delta^L_{n}|$$, where $$\delta^L_{k}$$ is the coefficient of $x^k$. 
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