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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2013, Volume 16, Issue 1, Pages 42–60 (Mi adm433)

RESEARCH ARTICLE

Labelling matrices and index matrices of a graph structure

T. Dinesha, T. V. Ramakrishnanb

a Department of Mathematics, Nehru Arts and Science College, Padannakkad P.O., Kasaragod District - 671 314, Kerala, India
b Department of Mathematics, S.E.S. College, Sreekandapuram, Kannur District - 670 631, Kerala, India

Abstract: The concept of graph structure was introduced by E. Sampathkumar in 'Generalised Graph Structures', Bull. The concept of graph structure was introduced by E. Sampathkumar in 'Generalised Graph Structures', Bull. Kerala Math. Assoc., Vol. 3, No. 2, Dec 2006, 65-123. Based on the works of Brouwer, Doob and Stewart, R.H. Jeurissen has ('The Incidence Matrix and Labelings of a Graph', J. Combin. Theory, Ser. B30 (1981), 290-301) proved that the collection of all admissible index vectors and the collection of all labellings for $0$ form free $F$-modules ($F$ is a commutative ring). We have obtained similar results on graph structures in a previous paper. In the present paper, we introduce labelling matrices and index matrices of graph structures and prove that the collection of all admissible index matrices and the collection of all labelling matrices for $0$ form free $F$-modules. We also find their ranks in various cases of bipartition and char $F$ (equal to 2 and not equal to 2).

Keywords: Graph structure, $R_{i}$-labelling, $R_{i}$-index vector, admissible $R_{i}$-index vector, labelling matrix, index matrix, admissible index matrix.

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Bibliographic databases:
MSC: 05C07,05C78
Revised: 29.05.2012
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Citation: T. Dinesh, T. V. Ramakrishnan, “Labelling matrices and index matrices of a graph structure”, Algebra Discrete Math., 16:1 (2013), 42–60

Citation in format AMSBIB
\Bibitem{DinRam13} \by T.~Dinesh, T.~V.~Ramakrishnan \paper Labelling matrices and index matrices of a graph structure \jour Algebra Discrete Math. \yr 2013 \vol 16 \issue 1 \pages 42--60 \mathnet{http://mi.mathnet.ru/adm433} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184697}