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CAYLEY SIGNED GRAPHS ASSOCIATED WITH ABELIAN GROUPS

  • PRANJALI, PRANJALI (Department of Mathematics, University of Rajasthan) ;
  • KUMAR, AMIT (Department of Mathematics and Statistics, Banasthali Vidyapith) ;
  • YADAV, TANUJA (Department of Mathematics and Statistics, Banasthali Vidyapith)
  • Received : 2021.12.13
  • Accepted : 2022.03.09
  • Published : 2022.05.30

Abstract

The aim of author's in this paper is to study the Cayley graph in the realm of signed graph. Moreover, we have characterized generating sets and finite abelian groups that corresponds to balanced Cayley signed graphs. The notion of Cayley signed graph has been demonstrated with the ample number of examples.

Keywords

References

  1. A. Cayley, Desiderata and Suggestions; The Theory of Groups: Graphical Representation, American Journal of Mathematics 1 (1878), 174-176. https://doi.org/10.2307/2369306
  2. D. Cartwright and F. Harary, Structural Balance, A Generalization of Heider's Theory, Psychological Review 63 (1956), 277-293. https://doi.org/10.1037/h0046049
  3. F. Harary, Graph Theory, Addison-Wesley Publ. Comp. Reading, MA, 1969.
  4. F. Harary, On the Notion of Balance of a Signed Graph, Mich. Math. J. 2 (1953), 143-146. https://doi.org/10.1307/mmj/1028989917
  5. F. Heider, Attitudes and Cognitive Organizations, Psychological Review 51 (1946), 358-374. https://doi.org/10.1037/h0055425
  6. N. Jacobson, Lectures in Abstract Algebra, East-West Press P. Ltd., New Delhi, 1951.
  7. Pranjali and A. Kumar, Algebraic Signed Graphs: A Review, In: Shrimali P. and Shah N. (eds.), Recent Advancements in Graph Theory. CRC Press, New York, 2020, 260-271.
  8. Pranjali, A. Kumar and T. Yadav, Cayley Graphs Versus Algebraic Graphs, J. Indones. Math. Soc. 27 (2021), 130-136. https://doi.org/10.22342/jims.27.2.800.130-136
  9. D. Sinha, P. Garg, On the Unitary Cayley Signed Graphs, The Electronic Journal of Combinatorics 18 (2011), 229.
  10. D. Witte and J.A. Gallian, A Survey: Hamiltonian Cycles in Cayley graphs, Discrete Mathematics North Holland 51 (1984), 293-304.
  11. T. Zaslavsky, A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas, Electronic Journal of Combinatorics, Dynamic Surveys in Combinatorics #DS8 (2012), 1-346.
  12. T. Zaslavsky, Signed Analogs of Bipartite Graphs, Discrete Math. 179 (1998), 205-216. https://doi.org/10.1016/S0012-365X(96)00386-X