Labelling matrices and index matrices of a graph structure
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....
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2013 |
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Інститут прикладної математики і механіки НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152307 |
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| Cite this: | Labelling matrices and index matrices of a graph structure / T. Dinesh, T. V. Ramakrishnan // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 1. — С. 42–60. — Бібліогр.: 12 назв. — англ. |
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Dinesh, T. Ramakrishnan, T.V. 2019-06-09T17:13:28Z 2019-06-09T17:13:28Z 2013 Labelling matrices and index matrices of a graph structure / T. Dinesh, T. V. Ramakrishnan // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 1. — С. 42–60. — Бібліогр.: 12 назв. — англ. 1726-3255 2010 MSC:05C07,05C78. https://nasplib.isofts.kiev.ua/handle/123456789/152307 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). en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Labelling matrices and index matrices of a graph structure Article published earlier |
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Labelling matrices and index matrices of a graph structure |
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Labelling matrices and index matrices of a graph structure Dinesh, T. Ramakrishnan, T.V. |
| title_short |
Labelling matrices and index matrices of a graph structure |
| title_full |
Labelling matrices and index matrices of a graph structure |
| title_fullStr |
Labelling matrices and index matrices of a graph structure |
| title_full_unstemmed |
Labelling matrices and index matrices of a graph structure |
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labelling matrices and index matrices of a graph structure |
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Dinesh, T. Ramakrishnan, T.V. |
| author_facet |
Dinesh, T. Ramakrishnan, T.V. |
| publishDate |
2013 |
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English |
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Algebra and Discrete Mathematics |
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Інститут прикладної математики і механіки НАН України |
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Article |
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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).
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| issn |
1726-3255 |
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https://nasplib.isofts.kiev.ua/handle/123456789/152307 |
| citation_txt |
Labelling matrices and index matrices of a graph structure / T. Dinesh, T. V. Ramakrishnan // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 1. — С. 42–60. — Бібліогр.: 12 назв. — англ. |
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AT dinesht labellingmatricesandindexmatricesofagraphstructure AT ramakrishnantv labellingmatricesandindexmatricesofagraphstructure |
| first_indexed |
2025-12-01T20:42:24Z |
| last_indexed |
2025-12-01T20:42:24Z |
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1850860920873418752 |