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A class of directed graph, when their minimal polynomial of the adjacency matrix matches the characteristic polynomial
We consider an unweighted directed simple graph, G, with a Hamiltonian cycle.
Q. Assume that the adjacency matrix of G is non-singular. Do the characteristic and minimal polynomials of the ...
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Properties of graphs with Hankel-like adjacency matrix
I am having undirected graphs with adjacency matrices which have a regular Hankel-like form, e.g.,
$$A=\begin{pmatrix}0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & (6\times 0 \text{ ...
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Effect of removing a Hamiltonian cycle on the Laplacian spectrum
Notation: λmax is the largest eigenvalue of the Laplacian matrix of the graph G (aka the Laplacian index of G).
Now suppose G is a Hamiltonian graph with Hamiltonian cycle C.
...