A sum labelling of the crown graph and some families of graphs

Authors

Jacob Francis C. Burgos, De La Salle University, Manila
Francis Joseph H. Campena, 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

Archival Material/Manuscript

Publication Date

2016

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 f_q,p is a symmetric collection of cycles meeting at a common vertex. This graph 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 the ladder graph P₂ P_n is at most n, the 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., Campena, F. H., & Iriberri, A. V. (2016). A sum labelling of the crown graph and some families of graphs. Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/13456

Disciplines

Mathematics

Note

Undated; Publication/creation date supplied

Keywords

Graph theory; Vertex detectors

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