5-cycles and the Petersen graph
Matt DeVos, Vahan V. Mkrtchyan, Samvel S. Petrosyan
TL;DR
This paper proves that the Petersen graph is uniquely characterized among connected bridgeless cubic graphs by the property that all its 2-factors consist solely of 5-cycles.
Contribution
It establishes a new characterization of the Petersen graph based on 2-factors composed exclusively of 5-cycles.
Findings
Petersen graph is uniquely identified by its 2-factor cycle structure.
Connected bridgeless cubic graphs with all 2-factors as 5-cycles are isomorphic to the Petersen graph.
The result provides a novel characterization of the Petersen graph in graph theory.
Abstract
We show that if G is a connected bridgeless cubic graph whose every 2-factor is comprised of cycles of length five then G is the Petersen graph.
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Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems · Rings, Modules, and Algebras