Cayley Graphs Versus Algebraic Graphs

Pranjali Pranjali; Amit Kumar; Tanuja Yadav

doi:10.22342/jims.27.2.800.130-136

Pranjali Pranjali ⁽¹⁾ , Amit Kumar ⁽²⁾ , Tanuja Yadav ⁽³⁾

(1) University of Rajasthan, India,

(2) Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali-304022, India., India,

(3) Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali-304022, India., India

https://doi.org/10.22342/jims.27.2.800.130-136

Issue
VOLUME 27 NUMBER 2 (July 2021)

Submitted
January 22, 2019

Accepted
April 5, 2021

Published
July 16, 2021

PDF

Abstract

Let Γ be a finite group and let S ⊆ Γ be a subset. The Cayley graph, denoted byCay(Γ, S) has vertex set Γ and two distinct vertices x, y ∈ Γ are joined by a directed edge fromx to y if and only if there exists s ∈ S such that x = sy. In this manuscript, we characterize the generating setsS for which Cay(Γ, S) is isomorphic to somealgebraic graphs, namely, unit graphs, co-unit graphs, total graph and co-total graphs.

Full text article

Generated from XML file

References

Beny, G. A. and Rakhmonov, Z., Number of Cayley graph of finite group Zn that is undirected, Proceedings of third Conference and Workshop on Group theory, University of Tehran, 9-10 March (2011), 8-11.

Cayley, A., Desiderata and suggestions; The Theory of groups: graphical representation, American Journal of Mathematics, 1(2 (1878), 174–176.

Harary, F., Graph Theory, Addison-Wesley Publ. Comp. Reading. MA, 1969.

Jacobson, N., Lectures in Abstract Algebra, East-West Press P. Ltd., New Delhi, 1951.

Maimani, H. R., Pournaki, M. R., Tehranian, A. and Yassemi, S. Graphs Attached to Rings

Revisited, Arabian Journal for Science and Engineering (2011), 36:997

Authors

Pranjali Pranjali

University of Rajasthan

pranjali48@gmail.com (Primary Contact)

Amit Kumar

Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali-304022, India.

Tanuja Yadav

Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali-304022, India.

Pranjali, P., Kumar, A., & Yadav, T. (2021). Cayley Graphs Versus Algebraic Graphs. Journal of the Indonesian Mathematical Society, 27(2), 130–136. https://doi.org/10.22342/jims.27.2.800.130-136