Combinatorics and Graph Theory

   

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

Unique-IP document downloads: 355 times

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