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....
Gespeichert in:
| Datum: | 2018 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/754 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-754 |
|---|---|
| record_format |
ojs |
| spelling |
admjournalluguniveduua-article-7542018-04-26T01:26:05Z Labelling matrices and index matrices of a graph structure Dinesh, T. Ramakrishnan, T. V. Graph structure, \(R_{i}\)-labelling, \(R_{i}\)-index vector, admissible \(R_{i}\)-index vector, labelling matrix, index matrix, admissible index matrix 05C07,05C78 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). Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/754 Algebra and Discrete Mathematics; Vol 16, No 1 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/754/283 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-04-26T01:26:05Z |
| collection |
OJS |
| language |
English |
| topic |
Graph structure \(R_{i}\)-labelling \(R_{i}\)-index vector admissible \(R_{i}\)-index vector labelling matrix index matrix admissible index matrix 05C07,05C78 |
| spellingShingle |
Graph structure \(R_{i}\)-labelling \(R_{i}\)-index vector admissible \(R_{i}\)-index vector labelling matrix index matrix admissible index matrix 05C07,05C78 Dinesh, T. Ramakrishnan, T. V. Labelling matrices and index matrices of a graph structure |
| topic_facet |
Graph structure \(R_{i}\)-labelling \(R_{i}\)-index vector admissible \(R_{i}\)-index vector labelling matrix index matrix admissible index matrix 05C07,05C78 |
| format |
Article |
| author |
Dinesh, T. Ramakrishnan, T. V. |
| 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 |
| 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). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/754 |
| work_keys_str_mv |
AT dinesht labellingmatricesandindexmatricesofagraphstructure AT ramakrishnantv labellingmatricesandindexmatricesofagraphstructure |
| first_indexed |
2025-12-02T15:36:55Z |
| last_indexed |
2025-12-02T15:36:55Z |
| _version_ |
1850411388359409664 |