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 Department

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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Embargo Period

5-22-2022

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