A sum labelling for some families of unicyclic graphs

Authors

Jacob Francis C. Burgos, De La Salle University, Manila
Francis Joseph H. Campeña, De La Salle University, Manila
Albert Nick V. Iriberri, De La Salle University, Manila

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

Manila Journal of Science

Volume

10

First Page

16

Last Page

24

Publication Date

2017

Abstract

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 f_q,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 T_n,m and the graph S_mC_n is at most 2 and that the crown graph 𝐶^k_𝑛 has a 1-optimal sum labelling.

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Recommended Citation

Burgos, J. C., Campeña, F. H., & Iriberri, A. V. (2017). A sum labelling for some families of unicyclic graphs. Manila Journal of Science, 10, 16-24. Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/11207

Disciplines

Mathematics

Keywords

Graph labelings; Graph theory

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