On the characteristic polynomial of the power of a path.
Keywords:Power of a path, 4-cycles, Characteristic coefficients
AbstractWe determine a closed-form expression for the ?fth characteristic coe?cient 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 modi?ed to count cycles of di?erent length.
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