## 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

**Download:** **PDF**

### Submission history

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

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

**Unique-IP document downloads:** 163 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*