Journal of Prime Research in Mathematics

# A cycle or Jahangir ramsey unsaturated graphs

Kshif Ali
School of Mathematical Science, GC University, Lahore, 68-B, New Muslim Town,
Lahore, Pakistan.
Surahmat
Department of Mathematics Education, Universitas Islam Malang, Jalan MT Haryono 193, Malang 65144, Indonesia.

$$^{1}$$Corresponding Author: akashif@sms.edu.pk.

### Abstract

A graph is Ramsey unsaturated if there exists a proper supergraph of the same order with the same Ramsey number, and Ramsey saturated otherwise. We present some result concerning both Ramsey saturated and unsaturated graph. In particular, we show that a cycle $$C_{n}$$ and a Jahangir $$J_{m}$$ Ramsey unsaturated or saturated graphs of $$R(C_n, W_m)$$ and $$R(P_n, J_m)$$, respectively. We also suggest an open problems.

#### Keywords:

Ramsey number, cycle, wheel, Jahangir, unsaturated.