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Properties of Digraphs Associated With Finite Cyclic Groups
Jimly Manuel1 , Bindhu K Thomas2
Section:Research Paper, Product Type: Journal-Paper
Vol.6 ,
Issue.5 , pp.52-56, Oct-2019
CrossRef-DOI: https://doi.org/10.26438/ijsrmss/v6i5.5256
Online published on Oct 31, 2019
Copyright © Jimly Manuel, Bindhu K Thomas . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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IEEE Style Citation: Jimly Manuel, Bindhu K Thomas, “Properties of Digraphs Associated With Finite Cyclic Groups,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.5, pp.52-56, 2019.
MLA Style Citation: Jimly Manuel, Bindhu K Thomas "Properties of Digraphs Associated With Finite Cyclic Groups." International Journal of Scientific Research in Mathematical and Statistical Sciences 6.5 (2019): 52-56.
APA Style Citation: Jimly Manuel, Bindhu K Thomas, (2019). Properties of Digraphs Associated With Finite Cyclic Groups. International Journal of Scientific Research in Mathematical and Statistical Sciences, 6(5), 52-56.
BibTex Style Citation:
@article{Manuel_2019,
author = {Jimly Manuel, Bindhu K Thomas},
title = {Properties of Digraphs Associated With Finite Cyclic Groups},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {10 2019},
volume = {6},
Issue = {5},
month = {10},
year = {2019},
issn = {2347-2693},
pages = {52-56},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1511},
doi = {https://doi.org/10.26438/ijcse/v6i5.5256}
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v6i5.5256}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1511
TI - Properties of Digraphs Associated With Finite Cyclic Groups
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Jimly Manuel, Bindhu K Thomas
PY - 2019
DA - 2019/10/31
PB - IJCSE, Indore, INDIA
SP - 52-56
IS - 5
VL - 6
SN - 2347-2693
ER -
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Abstract :
Studies have been made to investigate the relation between finite cyclic group and the associated digraph. Let be the cyclic group of order . The corresponding digraph is a simple digraph with vertex set equal to and two distinct vertices are joined by an arc from to if and only if there exists such that . In this paper we present some basic results on these digraphs associated with the cyclic group . The connection between group theoretical properties of the cyclic group and the structural properties of are investigated. The structure of digraph using generators of cyclic group are studied and established some results connecting degrees of the vertices of the digraph and the generators of the corresponding cyclic group. We also studied about the connectedness, condensation and point basis of this digraph.
Key-Words / Index Term :
Cyclic Group , Digraph , Connectedness, Condensation, Point Basis
References :
[1] F Harary, Graph Theory, Narosa Publishing House, 2001
[2] John B. Fraleigh, A first course in Abstract Algebra, Seventh edition, Pearson
[3] Moharram N. Iradmusaand Cheryl E. Praeger, Two-Sided Group Digraphs and Graphs, Journal of Graph Theory , Vol 82, Issue 3, Pages 279-295.
[4] R. Baalakrishnan, K. Ranganathan, A Textbook of Graph Theory, Second edition.
[5] Sonja Willis, Hamiltonian Paths and Cayley Digraphs of Algebraic Groups, UCSD Honors Thesis 2001.
[6] G Sabidussi, Graphs with given group and given graph- theoretical properties Canad. J. Math., 9 (1957), pp. 515-525
[7] R Frucht, Graphs of degree three with a given abstract group, Canad. J. Math., 1 (1949), pp. 365-378
[8] Sergei Silvestrov , Generating sets, Cayley digraphs. Groups of permutations as Universal model. Cayley’s theorem, Spring term 2011, lecture 10.
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