Chromatic Number of the Cyclic Graph of Infinite Semigroup

  • Sandeep Dalal
  • Jitender KumarEmail author
Original Paper


The cyclic graph \(\Gamma (S)\) of a semigroup S is the simple graph whose vertex set is S, two element being adjacent if the subsemigroup generated by these two elements is monogenic. The purpose of this note is to prove that the chromatic number of \(\Gamma (S)\) is at most countable. The present paper generalizes the results of Shitov (Graphs Comb 33(2):485–487, 2017) and the corresponding results on power graph and enhanced power graph of groups obtained by Aalipour et al. (Electron J Comb 24(3):#P3.16, 2017).


Monogenic semigroup Cyclic graph Power graph Enhanced power graph 

Mathematics Subject Classification




The authors are very grateful to the referees for their valuable suggestions which lead to an improvement of this paper. The second author wishes to acknowledge the support of MATRICS Grant (MTR/2018/000779) funded by SERB.


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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsBirla Institute of Technology and Science PilaniPilaniIndia

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