# Some formulas and bounds for the bandwidth of graphs

## Date of Publication

1999

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy in Mathematics

## Subject Categories

Mathematics

## College

College of Science

## Department/Unit

Mathematics and Statistics

## Thesis Adviser

Severino V. Gervacio

## Defense Panel Chair

Leonor A. Ruivivar

## Defense Panel Member

Severino D. Diesto

Blessilda P. Raposa

Yolando B. Beronque

Arlene A. Pascasio

## Abstract/Summary

The bandwidth problem for a graph is that of labeling its vertices with distinct integers so that the maximum difference across an edge is minimized. In this study, this problem is solved for the graph called flowerette Fn defined by Fortes [9] for all values of n. This is a graph which consists of the vertices of the cycle Cn together with copies of these vertices joined to each adjoining neighbor of the vertices of Cn. Furthermore, this problem is also solved for the Cartesian product of a doublestar Dm1,m2 with a path Pn, caterpillar T with a path Pn where n is greater than or equal to 2diamT - 1, caterpillar T with a cycle Cn, where n is greater than or equal to 4diamT and a connected graph G which is not complete with Pk/n where n is greater than or equal to k2(G)diamG. Optimal labellings to achieve each of these bandwidths are provided. In addition to these, some new bounds for the bandwidth of graphs are also given.

## Abstract Format

html

## Language

English

## Format

## Accession Number

TG02847

## Shelf Location

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

## Physical Description

79 leaves ; Computer print-out

## Keywords

Mathematics--Formulae; Graph theory; Mathematics--Problems, exercises, etc.

## Recommended Citation

Lim, Y. F. (1999). Some formulas and bounds for the bandwidth of graphs. Retrieved from https://animorepository.dlsu.edu.ph/etd_doctoral/804