On the planarity of paths, cycles, and wheels under some graph operations

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ID: 286831
2025
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Abstract
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 ๐‘› โ‰ค 9, only ๐พ1,1,1, ๐พ2,2,2, ๐พ2,3,3, and ๐พ3,3,3 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, ๐‘ƒ๐‘›๐‘˜, ๐ถ๐‘›๐‘˜, and ๐‘Š๐‘›๐‘˜, and the graph complements ๐‘ƒ๐‘›, C๐‘›, and W๐‘›.
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Authors Friborg, Gert Daniel Lacson
Journal Malay Journal
Year 2025
DOI
DOI not found
URL
https://animorepository.dlsu.edu.ph/etdb_math/52
Keywords Keywords not found

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