A class of intersection graph of half-lines and of line segments in the plane
The intersection graph of a non-empty family L of line segments in the plane, denoted by (L), is defined 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...
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| Format: | text |
| Language: | English |
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Animo Repository
2009
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_doctoral/238 https://animorepository.dlsu.edu.ph/context/etd_doctoral/article/1237/viewcontent/CDTG004564_P.pdf |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | The intersection graph of a non-empty family L of line segments in the plane, denoted by (L), is defined 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 φ-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 < φ < π ) 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 effects of other graph operations such as cartesian product, conjunction, composition and power on some special graphs. |
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