Cayley Coset Digraphs

Authors

  • Sujatha Suram Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, A.P., India. and Lecturer in Mathematics, General Section, Government Polytechnic, Vempall1-516329, A.P., India
  • Madhavi Levaku Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, A.P., India

DOI:

https://doi.org/10.14738/aivp.1402.20191

Keywords:

Digraph, Cayley coset digraph, vertex transitivity, connected graph, complete graph, loop, parallel edges

Abstract

In this paper, a new class of digraphs, namely, Cayley coset digraphs  associated with a group , a subgroup  and a subset  of  is introduced and it is shown that it is vertex transitive. Further the conditions under which this digraph is connected, complete and has loops and parallel edges are obtained.

References

Berrizbietia, P. and Giudici, R.E., Counting Pure k-Cycles in sequences of Cayley graphs, Discrete Math., 149, 11-18 (1996).

Berrizbietia, P. and Giudici, R.E., On Cycles in The sequence of Unitary Cayley graphs, Reporte Technico No. 01-95, Universidad Simon Bolivar, Dpt. De Mathematics Caracas, Venezla (1997).

Bhattacharya, P., Jain, S.K., and S.R. Naugpaul., Abstract Algebra 2/e Cambridge University Press, (1997).

Bondy J.A., and U.S.R. Murthy, Graph Theory and related topics, Acad. Press, New York

Cai Heng Li ., Lecture notes on Cayley graphs and coset graphs, (on line article), (2001).

Dejter J. and Giudici, R. E., On Unitary Cayley graphs, IJCMCC, 18, 121-124 (1995).

Devendra. J., Studies on the Domination Parameters and Cycle Structures of the Zero-Divisor Cayley Graph of the Residue Class Ring (Z ,⊕,⨀), Ph.D. Thesis, Yogi Vemana University, n Kadapa, India (2020).

Emanuel Knill., Notes on connectivity of Cayley coset digraphs, arXiv:math.Co / 94112 v1 10 Nov 1994.

Frank, Harary., Graph theory , Addison Wesley , Reading (1969). Scholar Publishing

Frucht, R., Herstellung von graphen mit vorgegebener abstakten Gruppe, Compositio . Math . 6 (1938), pp 239-250.

Herstein. I.N. Topics in Algebra, 2/e, Vikas Publishing House Private Limited, New Delhi.

Imrich.W., and Watkins., on automorphism of groups of Cayley graphs, period. Math.Hungar.7 (1976), 243-258.

Joy Morris., Connectvity of Cayley graphs : A special family, (A survey article) Dept. of Mathematics and Statistics ,Trent University, Peterborough, (2004).

Konig.D., Theorie der endlichen und unendlichen Graphen,Leipzig (1936), Reprinted Chelsea , New York (1950).

Kurcz. R., Closed Walks in Coset Graphs and Vertex-Transitive Non-Cayley Graphs, Acta Math. Univ. Comenianae, Vol. LXVIII, 1 (1999), pp. 127-135.

Madhavi. L., Studies on Domination Parameters and Enumeration of Cycles in some Arithmetic Cayley Graphs, Ph.D. Thesis, Sri Venkateswara University, Tirupati, India (2003).

Nagalakshumma. T., Studies on the Nilpotent Cayley Graph of the Residue Class Ring (Z ,⊕,⨀) and its Neighbourhood Graph, Ph.D. Thesis, Yogi Vemana University, Kadapa, India n

Narsing Deo., Graph Theory with applications to engineering and computer science, Prentice-Hall of India Privte Ltd, New Delhi (1995).

Parthasarathy K.R., Basic graph Theory, Tata Mc.Graw-Hill Publishing Company Limited

Robert Rosiek, Mariusz Wozniak., A note introducing Cayley graphs and group-coset graphs generated by graph packings, Opuscula Mathematica. Vol 24/2 (2004).

Venkat Subbaiah. P., Studies on Cayley Conjugate Digarphs and Conjugate Coset Digraphs, Ph.D. Thesis, Sri Venkateswara University, Tirupati, India (2009).

Yunsun Nam., Isomorphism classes of Cayley permutation graphs, J. Korean Math. Soc. 34 (1997), No.2, pp. 337-344.

Downloads

Published

2026-04-10

How to Cite

Suram, S., & Levaku, M. (2026). Cayley Coset Digraphs. European Journal of Applied Sciences, 14(02), 245–256. https://doi.org/10.14738/aivp.1402.20191