# A sum labelling for some families of unicyclic graphs

## 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_{m}C_{n} is at most 2 and that the crown graph 𝐶^{k}_{𝑛} has a 1-optimal sum labelling.

html

## 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

## Upload File

wf_no