## Matrix Determinant as a Verifier of a Path (Cycle) in the Directed Hamiltonian Cycle Problem Under Two Special Conditions: a Formal Proof

**Authors:** Okunoye Babatunde

In earlier work, the author conjectured that under two special conditions relating to theorems on the determinant of a matrix: the absence of a zero row (column) and the absence of similar rows (columns), a non-zero determinant value certifies the existence of a Directed Hamiltonian Path in an arbitrary adjacency matrix. Here, a formal proof is provided by means of deductive logic to establish that in an arbitrary adjacency matrix of size n (n rows and n columns), a non-zero determinant value verifies the existence of a Directed Hamiltonian Path in the adjacency matrix

**Comments:** 4 Pages. Accepted and Revised at IEEE African Journal of Computing and ICTs

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### Submission history

[v1] 2012-09-06 18:40:36

[v2] 2012-09-11 22:39:16

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