Continuant, caterpillar, and topological index Z. III. Graph-theoretical algorithm for and interpretation of solving linear Diophantine equations

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  • Continuant caterpillar and topological index Z 3 Graph theoretical algorithm for and interpretation of solving linear Diophantine equations

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The conventional algorithm for solving the linear Diophantine equation in two variables is greatly improved graph-theoretically by using the Z-caterpillars, namely, by substituting all the relevant series of integers with the caterpillar graphs whose topological indices represent those integers. By this graph-theoretical analysis, the mathematical structure of the linear Diophantine equation and its relation with the Euclid's algorithm, continued fraction, and Euler's continuant are clarified.

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