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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1327-1331
http://dx.doi.org/10.1155/IJMMS.2005.1327

The complete product of annihilatingly unique digraphs

Faculty of Engineering and Technology, Multimedia University, Malacca 75450, Malaysia

Received 25 February 2005; Revised 10 May 2005

Copyright © 2005 C. S. GAN. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let G be a digraph with n vertices and let A(G) be its adjacency matrix. A monic polynomial f(x) of degree at most n is called an annihilating polynomial of G if f(A(G))=0. G is said to be annihilatingly unique if it possesses a unique annihilating polynomial. Difans and diwheels are two classes of annihilatingly unique digraphs. In this paper, it is shown that the complete product of difan and diwheel is annihilatingly unique.