Induced subgraphs of Johnson graphs (JIS for short) were studied first time in 2010 by R. Naimi and Jaffrey Shaw. They gave some necessary conditions and some sufficient conditions for a graph to be JIS. We have obtained some results which help to decide whether a given graph is JIS or not and have been able to find some new sufficient conditions for a graph to be JIS. We, also classified all graphs of order less than 6 or size less than 7 into JIS and non-JIS category. Furthermore, we give some special JIS graphs as well as non-JIS graphs. Ramin Naimi and Jaffrey Shaw proposed a conjecture The graph p is JIS if and only if p is odd. We have attacked this conjecture and have been able to prove that If p is odd then p is JIS.

Akbar Ali completed his M.Phil degree from University of the Punjab, Lahore-Pakistan in 2011. His research interest include Graph Theory and Mathematical Chemistry.