# Resistance distance in some composition of graphs

## Date of Publication

2014

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy in Mathematics

## College

College of Science

## Department/Unit

Mathematics and Statistics

## Thesis Adviser

Severino V. Gervacio

## Defense Panel Chair

Leonor Ruivivar

## Defense Panel Member

Emerlinda Fortes

Yvette F. Lim

Felix Muga

## Abstract/Summary

In graph theory, the resistance distance between any two vertices of a simple connected graph G is equal to the e ective resistance between two corresponding nodes on an electrical network, constructed so as to correspond to G, with each edge being replaced by a unit resistor or a 1 ohm resistance. This resistance is known to be a metric on a graph.

This paper aims to nd an explicit expression for the resistance distance between any pair of vertices in some composition of graphs. Speci cally, the e ective resis- tance between any two vertices in each graph of Pn[Km] Tn[Km] Cn[Km] Pn[Km] Tn[Km] Cn[Km] are determined.

The relationship between the resistance distance between two vertices in a graph and its complement will be investigated.

## Abstract Format

html

## Language

English

## Format

Electronic

## Accession Number

CDTG005789

## Shelf Location

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

## Physical Description

1 computer optical disc ; 4 3/4 in.

## Keywords

Graph theory

## Recommended Citation

Lubguban, A. A. (2014). Resistance distance in some composition of graphs. Retrieved from https://animorepository.dlsu.edu.ph/etd_doctoral/394