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

Date of Publication

2016

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Francis Joseph H. Campeña

Abstract/Summary

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 fq 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 Pn is at most n, the tadpole graph Tn m and the graph SmCn is at most 2 and that the crown graph Ckn has a 1-optimal sum labelling.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTU021091

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Keywords

Graph theory; Vertex detectors

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