In 2008, H. Fernau et al. provided an optimal sum labelling scheme of the generalized friendship graph and showed that its sum number is 2. The generalized friendship graph is a symmetric collection of cycles meeting at a common vertex. This graph fq,p may also be viewed as a graph obtained by considering several copies of a cycle and identifying a vertex from each cycle and merging them into a single vertex. In this paper, we consider a cycle and several paths and form a graph by concatenating a pendant vertex from a path to a vertex in the cycle. We also determine the exact value or a bound for the sum number of the resulting graph. Specifically, we show that the sum number of tadpole graph Tn,m and the graph SmCn is at most 2 and that the crown graph ckn has a 1-optimal sum labelling.