Research Article
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Year 2020, Volume 28, Issue 28, 110 - 126, 14.07.2020
https://doi.org/10.24330/ieja.768190

Abstract

References

  • M. Afkhami, H. Reza Barani, K. Khashyarmanesh and F. Rahbarnia, A new class of Cayley graphs, J. Algebra Appl., 15(4) (2016), 1650076 (8 pp).
  • Y. Chaiya, P. Honyam and J. Sanwong, Natural partial orders on transformation semigroups with fixed sets, Int. J. Math. Math. Sci., (2016), 2759090 (7 pp).
  • A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. I, Mathematical Surveys, 7, American Mathematical Society, Providence, R.I., 1961.
  • A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. II, Mathematical Surveys, 7, American Mathematical Society, Providence, R.I., 1967.
  • S. Fan and Y. Zeng, On Cayley graphs of bands, Semigroup Forum, 74(1) (2007), 99-105.
  • Y. Hao and Y. Luo, On the Cayley graphs of left (right) groups, Southeast Asian Bull. Math., 34(4) (2010), 685-691.
  • P. Honyam and J. Sanwong, Semigroups of transformations with fixed sets, Quaest. Math., 36(1) (2013), 79-92.
  • J. M. Howie, Fundamentals of Semigroup Theory, London Mathematical Society Monographs, New Series, 12, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995.
  • A. V. Kelarev, On Cayley graphs of inverse semigroups, Semigroup Forum, 72(3) (2006), 411-418.
  • B. Khosravi and M. Mahmoudi, On Cayley graphs of rectangular groups, Discrete Math., 310(4) (2010), 804-811.
  • Y. Luo, Y. Hao and G. T. Clarke, On the Cayley graphs of completely simple semigroups, Semigroup Forum, 82(2) (2011), 288-295.
  • R. P. Panda and K. V. Krishna, On connectedness of power graphs of finite groups, J. Algebra Appl., 17(10) (2018), 1850184 (20 pp).
  • S. Pirzada, An Introduction to Graph Theory, Universities Press, Orient Blackswan, India, 2012.
  • A. Riyas and K. Geetha, Some properties of Cayley graphs of full transformation semigroups, Int. J. Math. Archive, 9(4) (2018), 64-69.
  • D. Sinha and D. Sharma, Structural properties of absorption Cayley graphs, Appl. Math. Inf. Sci., 10(6) (2016), 2237-2245.
  • T. Suksumran and S. Panma, On connected Cayley graphs of semigroups, Thai J. Math., 13(3) (2015), 641-652.
  • C. Tisklang and S. Panma, On connectedness of Cayley graphs of finite transformation semigroups, Thai J. Math., Special issue (2018), 261-271.

ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS

Year 2020, Volume 28, Issue 28, 110 - 126, 14.07.2020
https://doi.org/10.24330/ieja.768190

Abstract

Let $\text{Fix}(X,Y)$ be a semigroup of full transformations on a set $X$ in which elements in a nonempty subset $Y$ of $X$ are fixed. In this paper, we construct the Cayley digraphs of $\text{Fix}(X,Y)$ and study some structural properties of such digraphs such as the connectedness and the completeness. Further, some prominent results of Cayley digraphs of $\text{Fix}(X,Y)$ relative to minimal idempotents are verified. In addition, the characterization of an equivalence digraph of the Cayley digraph of $\text{Fix}(X,Y)$ is also investigated.

References

  • M. Afkhami, H. Reza Barani, K. Khashyarmanesh and F. Rahbarnia, A new class of Cayley graphs, J. Algebra Appl., 15(4) (2016), 1650076 (8 pp).
  • Y. Chaiya, P. Honyam and J. Sanwong, Natural partial orders on transformation semigroups with fixed sets, Int. J. Math. Math. Sci., (2016), 2759090 (7 pp).
  • A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. I, Mathematical Surveys, 7, American Mathematical Society, Providence, R.I., 1961.
  • A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. II, Mathematical Surveys, 7, American Mathematical Society, Providence, R.I., 1967.
  • S. Fan and Y. Zeng, On Cayley graphs of bands, Semigroup Forum, 74(1) (2007), 99-105.
  • Y. Hao and Y. Luo, On the Cayley graphs of left (right) groups, Southeast Asian Bull. Math., 34(4) (2010), 685-691.
  • P. Honyam and J. Sanwong, Semigroups of transformations with fixed sets, Quaest. Math., 36(1) (2013), 79-92.
  • J. M. Howie, Fundamentals of Semigroup Theory, London Mathematical Society Monographs, New Series, 12, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995.
  • A. V. Kelarev, On Cayley graphs of inverse semigroups, Semigroup Forum, 72(3) (2006), 411-418.
  • B. Khosravi and M. Mahmoudi, On Cayley graphs of rectangular groups, Discrete Math., 310(4) (2010), 804-811.
  • Y. Luo, Y. Hao and G. T. Clarke, On the Cayley graphs of completely simple semigroups, Semigroup Forum, 82(2) (2011), 288-295.
  • R. P. Panda and K. V. Krishna, On connectedness of power graphs of finite groups, J. Algebra Appl., 17(10) (2018), 1850184 (20 pp).
  • S. Pirzada, An Introduction to Graph Theory, Universities Press, Orient Blackswan, India, 2012.
  • A. Riyas and K. Geetha, Some properties of Cayley graphs of full transformation semigroups, Int. J. Math. Archive, 9(4) (2018), 64-69.
  • D. Sinha and D. Sharma, Structural properties of absorption Cayley graphs, Appl. Math. Inf. Sci., 10(6) (2016), 2237-2245.
  • T. Suksumran and S. Panma, On connected Cayley graphs of semigroups, Thai J. Math., 13(3) (2015), 641-652.
  • C. Tisklang and S. Panma, On connectedness of Cayley graphs of finite transformation semigroups, Thai J. Math., Special issue (2018), 261-271.

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

Nuttawoot NUPO This is me (Primary Author)
Khon Kaen University
Thailand


Chollawat POOKPIENLERT This is me
Rajamangala University of Technology Lanna
Thailand

Publication Date July 14, 2020
Published in Issue Year 2020, Volume 28, Issue 28

Cite

Bibtex @research article { ieja768190, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2020}, volume = {28}, number = {28}, pages = {110 - 126}, doi = {10.24330/ieja.768190}, title = {ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS}, key = {cite}, author = {Nupo, Nuttawoot and Pookpıenlert, Chollawat} }
APA Nupo, N. & Pookpıenlert, C. (2020). ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS . International Electronic Journal of Algebra , 28 (28) , 110-126 . DOI: 10.24330/ieja.768190
MLA Nupo, N. , Pookpıenlert, C. "ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS" . International Electronic Journal of Algebra 28 (2020 ): 110-126 <https://dergipark.org.tr/en/pub/ieja/issue/55997/768190>
Chicago Nupo, N. , Pookpıenlert, C. "ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS". International Electronic Journal of Algebra 28 (2020 ): 110-126
RIS TY - JOUR T1 - ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS AU - NuttawootNupo, ChollawatPookpıenlert Y1 - 2020 PY - 2020 N1 - doi: 10.24330/ieja.768190 DO - 10.24330/ieja.768190 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 110 EP - 126 VL - 28 IS - 28 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.768190 UR - https://doi.org/10.24330/ieja.768190 Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Algebra ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS %A Nuttawoot Nupo , Chollawat Pookpıenlert %T ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS %D 2020 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 28 %N 28 %R doi: 10.24330/ieja.768190 %U 10.24330/ieja.768190
ISNAD Nupo, Nuttawoot , Pookpıenlert, Chollawat . "ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS". International Electronic Journal of Algebra 28 / 28 (July 2020): 110-126 . https://doi.org/10.24330/ieja.768190
AMA Nupo N. , Pookpıenlert C. ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS. IEJA. 2020; 28(28): 110-126.
Vancouver Nupo N. , Pookpıenlert C. ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS. International Electronic Journal of Algebra. 2020; 28(28): 110-126.
IEEE N. Nupo and C. Pookpıenlert , "ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS", International Electronic Journal of Algebra, vol. 28, no. 28, pp. 110-126, Jul. 2020, doi:10.24330/ieja.768190