%0 Journal Article
%T Aunu Integer Sequence as Non-Associative Structure and Their Graph Theoretic Properties
%A Aminu Alhaji Ibrahim
%A Sa¡¯idu Isah Abubaka
%J Advances in Pure Mathematics
%P 409-419
%@ 2160-0384
%D 2016
%I Scientific Research Publishing
%R 10.4236/apm.2016.66028
%X The generating function for generating integer sequence of Aunu numbers
of prime cardinality was reported earlier by the author in [1]. This paper assigns an operator ![\"\"](\"Edit_0ef2da4d-f89f-40d2-ade0-23ca47be57af.bmp\")
on the function ![\"\"](\"Edit_c0942648-9bcc-49bf-8bc3-38ab3a526cfc.bmp\")
for ![\"\"](\"Edit_5dad167f-5860-4f76-8017-da97cff8b627.bmp\")
where the operation
induces addition or subtraction on the pairs of ai, aj elements which are
consecutive pairs of elements obtained from a generating set ![\"\"](\"Edit_4a828102-9a03-4cab-882c-2d923d644505.bmp\")
of some finite order. The paper identifies
that the set of the generated pairs of integer sequence is
non-associative. The paper also presents the graph theoretic applications of
the integers generated in which subgraphs are deduced from the main graph and
adjacency matrices and incidence matrices constructed. It was also established
that some of the subgraphs were found to be regular graphs. The findings in
this paper can further be used in coding theory, Boolean algebra and circuit
designs.
%K Aunu Numbers
%K Nonassociative
%K Graph
%K Subgraphs
%K Adjacency Matrix
%K Incidence Matrix
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=66535