It is proved by counter example that one of the theorems presented in [FILOMAT 29:8 (2015), 1781- 1788] does not always hold true. It is also proved by counter example that the necessary condition given in Theorem 3.7 [If diam(H) = 2, then s(K1 ⊙H) = s(H)] mentioned in the above cited paper does not hold true.