On the characteristic polynomial of the power of a path.
Keywords:Power of a path, 4-cycles, Characteristic coefficients
We determine a closed-form expression for the fifth characteristic coefficient of the power of a path. To arrive at this result, we establish the number of 4-cycles in the graph by means of their structural properties. The method developed might be applied to other well-structured graph classes in order to count 4-cycles or modified to count cycles of different length.
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