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Irregular colorings of derived graphs of flower graph

Abstract

The concept of irregular coloring was established by Radcliffe and Zhang (AKCE J Graphs Combinator 3(2):175–191, 2006). Irregular coloring is a proper coloring, in which distinct vertices have different color codes. In this paper, we find the irregular chromatic number for the following graphs: \(M\left( F_{n}\right) \), \(T\left( F_{n}\right) \), \(L\left( F_{n}\right) \), \(C\left( F_{n}\right) \), \(M\left( J_{2,n}\right) \), \(T\left( J_{2,n}\right) \), \(L\left( J_{2,n}\right) \), \(C\left( J_{2,n}\right) \), \(M\left( W_{n}\right) \), \(T\left( W_{n}\right) \), \(L\left( W_{n}\right) \), \(C\left( W_{n}\right) \), \(M\left( B_{n}\right) \), \(T\left( B_{n}\right) \), \(L\left( B_{n}\right) \) and \(C\left( B_{n}\right) \).

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Correspondence to A. Rohini.

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Rohini, A., Venkatachalam, M. & Sangamithra, R. Irregular colorings of derived graphs of flower graph. SeMA 77, 47–57 (2020). https://doi.org/10.1007/s40324-019-00201-1

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Keywords

  • Irregular coloring
  • Middle graph
  • Total graph
  • Central graph
  • Line graph

Mathematics Subject Classification

  • 05C15