## Dissertations

2009

Dissertation

#### Degree Name

Doctor of Philosophy in Mathematics

Mathematics

#### College

College of Science

#### Department/Unit

Mathematics and Statistics Department

Severino V. Gervacio

#### Defense Panel Member

Yvette F. Lim
Leonor A. Ruivivar
Blessilda P. Raposa
Isagani B. Jos
Erminda Fortes,

#### Abstract/Summary

The intersection graph of a non-empty family L of line segments in the plane, denoted by (L), is de ned as the graph whose vertex-set is L, where there is an edge between two vertices `1 and `2 in L if `1 \ `2 6= . If L is a family of half-lines, (L) is called a half-line intersection graph. We de ne here a graph whose half-line representation L can be contained in an arbitrarily thin -slice of the plane (the convex subset of R2 bounded by two half-lines with a common end-point and making an angle of (radians) with each other, 0 < < ) as wedge graphs. We show that wedge graphs are closed under the graph operations union and join. We prove that wedge graphs are segment intersection graphs and unit intersection graphs. We also determine the e ects of other graph operations such as cartesian product, conjunction, composition and power on some special graphs.

html

English

Electronic

CDTG004564

#### Shelf Location

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

#### Physical Description

v, 71 leaves ; 28 cm.

#### Keywords

Intersection graph theory