Date of Publication
2020
Document Type
Master's Thesis
Degree Name
Master of Science in Mathematics
Subject Categories
Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Thesis Adviser
Francis Joseph Campeña
Abstract/Summary
A [1, 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and at most two neighbours in it. If the additional requirement that the set be independent is added, the existence of such a set is not guaranteed in every graph. In this paper, we study the existence of independent [1, 2]-sets in some classes of cactus graphs and determine such sets for some parameters of the graph. In particular, we will show that there exists an independent [1, 2]-set for any cactus graph with k ≥ 2 cycles, 2 and 3 as the minimum and maximum degree of a vertex in the cactus graph, respectively. We also study the minimum cardinality of an independent [1, 2]-set in some other classes of cactus graphs.
Abstract Format
html
Language
English
Format
Electronic
Physical Description
[vi], 56 leaves
Keywords
Charts, diagrams, etc; Graphic methods
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Recommended Citation
Chien, H. C. (2020). Independent [1,2]-sets in some classes of cactus graphs. Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/5984
Embargo Period
5-22-2022
