In the mathematical

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 field of graph theory

Graph theory

In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

, the double-star snark is a snark

Snark (graph theory)

In the mathematical field of graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to 4. In other words, it is a graph in which every vertex has three neighbors, and the edges cannot be colored by only three colors without two edges of the same color meeting at a...

 with 30 vertices

Vertex (graph theory)

In graph theory, a vertex or node is the fundamental unit out of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges , while a directed graph consists of a set of vertices and a set of arcs...

 and 45 edges.

In 1975, Rufus Isaacs introduced two infinite families of snarks—the flower snark

Flower snark

In the mathematical field of graph theory, the flower snarks form an infinite family of snarks introduced by Rufus Isaacs in 1975.As snarks, the flower snarks are a connected, bridgeless cubic graphs with chromatic index equal to 4...

 and the BDS snark, a family that includes the two Blanuša snarks

Blanuša snarks

In the mathematical field of graph theory, the Blanuša snarks are two 3-regular graphs with 18 vertices and 27 edges. They were discovered by Croatian mathematician Danilo Blanuša in 1946 and are named after him. When discovered, only one snark was known—the Petersen graph.As snarks, the Blanuša...

, the Descartes snark

Descartes snark

In the mathematical field of graph theory, a Descartes snark is an undirected graph with 210 vertices and 315 edges. It is a snark, first discovered by William Tutte in 1948 under the pseudonym Blanche Descartes....

 and the Szekeres snark

Szekeres snark

In the mathematical field of graph theory, the Szekeres snark is a snark with 50 vertices and 75 edges. It was the fifth known snark, discovered by George Szekeres in 1973....

 (BDS stands for Blanuša Descartes Szekeres). Isaacs also discovered one 30-vertex snark that does not belongs to the BSD family and that is not a flower snark — the double-star snark.

As a snark, the double-star graph is a connected, bridgeless cubic graph

Cubic graph

In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs....

 with chromatic index equal to 4. The double-star snark is non-planar

Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints...

 and non-hamiltonian but is hypohamiltonian

Hypohamiltonian graph

In the mathematical field of graph theory, a graph G is said to be hypohamiltonian if G does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex from G is Hamiltonian.-History:...

.