# On The Transformation and Transformation Number of Special Graphs

Good Essays
Topics: Graph theory
On The Transformation and
Transformation Number of Special Graphs

A Special Problem
Presented to the Faculty of the
Department of Mathematics and Statistics
College of Arts and Sciences
University of Southeastern Philippines

In Partial Fulﬁllment of the Requirements for the Degree of
Bachelor of Science in Mathematics

Romelyn D. Villamor
April 2009

Abstract

This paper introduces a new operation on graphs called transformation. A transformation is applicable on simple connected graphs. A onetransformation of a graph G is a graph obtained by joining pairs of nonadjacent vertices of G resulting to an increase in the degree of each vertex by one. If the graph can have a one-transformation then the graph is a onetransformer or a transformer. An n-transformation of a graph G is obtained by performing n number of one-transformation on G. A graph is n-transformer if it can perform n number of one-transformation.
This paper presents the transformation and the transformation number of some special graphs such as path graphs, cycle graphs, complete bipartite graphs, fans, and generalized fans.

To my family

and

friends this work is whole-heartedly dedicated. . . .

“It is good to give thanks to the Lord, to sing praise to your name, Most
High. . . ”
Psalm 92:2

Page
Title Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i Approval Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Bibliography: [1] Behzad, M. and Chartrand G., Introduction to the Graph Theory, Allyn and Bocon Publishing Co., Inc., 1971. [2] Berge, C., Graphs and Hypergraphs, Amsterdam Publishing Co.,Inc., 1973. [3] Bondy, J.A. and Murty U.S.R, Graph Theory with Applications, Elsevier Science Publishing Co., Inc., 1982. [4] Harary, F., Graph Theory, Addison-Wesley Publishing Company, Inc., 1969. [5] Lui, C.L., Introduction to Combinatorial Mathematics, McGraw-Hill Publishing Co., Inc., 1968. [6] Ore, O., Graph and Their Uses, Random House Publishing Co., Inc., 1963. [7] Wilson, R.J., Introduction to Graph Theory, Oliver and Boyd Publishing Co., Inc., 1972.

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