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There are several different definitions of the barbell graph. Most commonly and in this work, the n-barbell graph is the simple graph obtained by connecting two copies of a ...

Let A be an edge cut of a connected graph G. Then the cyclic edge connectivity lambda_c(G) is the size of a smallest cyclic edge cut, i.e., a smallest edge cut A such that ...

The edge chromatic number, sometimes also called the chromatic index, of a graph G is fewest number of colors necessary to color each edge of G such that no two edges ...

A (general, asymmetric) lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely ...

A lune is a plane figure bounded by two circular arcs of unequal radii, i.e., a crescent. (By contrast, a plane figure bounded by two circular arcs of equal radius is known ...

The term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two equal circles whose centers are offset ...

There are a number of meanings for the word "arc" in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length. ...

The Celmins-Swart snarks are the two snarks on 26 vertices and 39 edges illustrated above. They are implemented in the Wolfram Language as GraphData["CelminsSwartSnark1"] and ...

Cubic nonhamiltonian graphs are nonhamiltonian graphs that are also cubic. The numbers of connected cubic nonhamiltonian graphs on n=10, 12, ... nodes are 2, 5, 35, 219, ...

The helm graph H_n is the graph obtained from an n-wheel graph by adjoining a pendant edge at each node of the cycle. Helm graphs are graceful (Gallian 2018), with the odd ...