A sum labelling for some families of unicyclic graphs

• Main Authors: Burgos, Jacob Francis C., Campeña, Francis Joseph H., Iriberri, Albert Nick V.
• Format: text
• Published: Animo Repository 2017
• Subjects: Graph labelings; Graph theory; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/11207
• Institution: De La Salle University

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.