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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| Дата: | 2013 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2013
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152307 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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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irk-123456789-1523072019-06-10T01:25:28Z Labelling matrices and index matrices of a graph structure Dinesh, T. Ramakrishnan, T.V. 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). 2013 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/152307 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
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). |
| format |
Article |
| author |
Dinesh, T. Ramakrishnan, T.V. |
| spellingShingle |
Dinesh, T. Ramakrishnan, T.V. Labelling matrices and index matrices of a graph structure Algebra and Discrete Mathematics |
| author_facet |
Dinesh, T. Ramakrishnan, T.V. |
| author_sort |
Dinesh, T. |
| title |
Labelling matrices and index matrices of a graph structure |
| 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 |
| title_sort |
labelling matrices and index matrices of a graph structure |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
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2023-05-20T17:38:01Z |
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