Graphs with equal girth and circumference
Lewis Stanton, Jeffrey Thompson
TL;DR
This paper characterizes all finite simple graphs where the girth equals the circumference and establishes a bound on their number of edges, advancing understanding of their structural properties.
Contribution
It provides a complete characterization of graphs with equal girth and circumference and derives a new bound on their edges.
Findings
Characterization of graphs with equal girth and circumference
A proven bound on the number of edges in such graphs
Insights into the structural properties of these graphs
Abstract
We characterise the form of all simple, finite graphs for which the girth of the graph is equal to the circumference of the graph. We apply this to prove a bound on the number of edges in such a graph.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Graph Labeling and Dimension Problems