Date of Publication

8-2025

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with Specialization in Computer Applications

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

Severino V. Gervacio

Defense Panel Chair

Isagani B. Jos

Defense Panel Member

Rigor B. Ponsones

Abstract/Summary

Graphs that can be represented on a flat surface without any edge crossings are called planar. Alongside numerous practical applications, previous studies also characterized planar graphs and presented constructions for various larger planar graphs, with the latter introducing graph operations: adding an edge, adding a pair of edges, and replacing a region. The research that inspired this paper showed that for complete tripartite graphs of order 𝑛 ≀ 9, only 𝐾1,1,1, 𝐾2,2,2, 𝐾2,3,3, and 𝐾3,3,3 contain a spanning maximal planar graph, which was followed by another study that extended their work to complete 4-partite graphs. The proposed research then aims to determine the maximum size of the spanning planar subgraphs of paths, cycles, and wheels, when transformed by graph powers and graph complements. In particular, we present results on the maximal spanning planar subgraphs of the graph powers, π‘ƒπ‘›π‘˜, πΆπ‘›π‘˜, and π‘Šπ‘›π‘˜, and the graph complements 𝑃𝑛, C𝑛, and W𝑛.

Abstract Format

html

Language

English

Format

Electronic

Keywords

Graph theory

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Embargo Period

8-11-2026

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Available for download on Tuesday, August 11, 2026

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