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Abstract
The aim of this work is to give a definition of the incidence matrices of the directed graph of groups, construct an up-down pregroup of the incidence matrices of the directed graph of groups and then give an algorithm for the up-down pregroup of the directed graph of groups.
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References
- Jassim, W.S. Incidence Matrices of X-Labeled Graphs and an application, Sultan Qaboos University Journal for Science, 2009, 14, 61-69.
- Hoare, A.H.M. and Jassim, W.S. Directed graphs of groups and their up-down pregroups, Faculty of Science Bulletin, Sana'a University, 2004, 17, 137-154.
- Jassim, W.S. Pregroups and graphs of groups, Ph.D. Thesis, Birmingham University, 1992.
- Rimlinger, F. Pregroups and Bass – Serre theory. American Mathematical Society Memoirs, 1987.
- Baer, R. Free Sums of groups and their generalizations III. American Journal of Mathematics, 1950, 647-670.
- Stallings, J.P. Group theory and Three dim. Manifolds. Yale Monographs, 1971.
- Hoare, A.H.M. Pregroups and Length functions. Proceedings of the Cambridge Philosophical Society. 1988, 21-30.
- Stallings, J.P. Adyan Groups and Pregroups, Essays in group theory, MSRI Publications 8ed. By S.M. Gersten, 1987.
- Abdu, K.A. Representing Core graphs and Nickolas's Algorithm. M.Sc. Thesis, Baghdad University, 1999.
- Chiswell, I.M. Abstract Length functions in groups. Proceedings of the Cambridge Philosophical Society. 1976, 417-429.
- Jassim, W.S. Directed Core Graphs and their up-down pregroups, Al-Mustansiriya Journal of Science, 2006, 17(4): 68-81.
- Lyndon, R.C. Length functions in groups. Mathematica Scandinavica, 1963, 209-234.
- Serre, J.P. 1968. Groupes discrets. College de France. Translation, Trees. Springer Verlag, 1980.
References
Jassim, W.S. Incidence Matrices of X-Labeled Graphs and an application, Sultan Qaboos University Journal for Science, 2009, 14, 61-69.
Hoare, A.H.M. and Jassim, W.S. Directed graphs of groups and their up-down pregroups, Faculty of Science Bulletin, Sana'a University, 2004, 17, 137-154.
Jassim, W.S. Pregroups and graphs of groups, Ph.D. Thesis, Birmingham University, 1992.
Rimlinger, F. Pregroups and Bass – Serre theory. American Mathematical Society Memoirs, 1987.
Baer, R. Free Sums of groups and their generalizations III. American Journal of Mathematics, 1950, 647-670.
Stallings, J.P. Group theory and Three dim. Manifolds. Yale Monographs, 1971.
Hoare, A.H.M. Pregroups and Length functions. Proceedings of the Cambridge Philosophical Society. 1988, 21-30.
Stallings, J.P. Adyan Groups and Pregroups, Essays in group theory, MSRI Publications 8ed. By S.M. Gersten, 1987.
Abdu, K.A. Representing Core graphs and Nickolas's Algorithm. M.Sc. Thesis, Baghdad University, 1999.
Chiswell, I.M. Abstract Length functions in groups. Proceedings of the Cambridge Philosophical Society. 1976, 417-429.
Jassim, W.S. Directed Core Graphs and their up-down pregroups, Al-Mustansiriya Journal of Science, 2006, 17(4): 68-81.
Lyndon, R.C. Length functions in groups. Mathematica Scandinavica, 1963, 209-234.
Serre, J.P. 1968. Groupes discrets. College de France. Translation, Trees. Springer Verlag, 1980.