| Double-star snark | |
|---|---|
 The Double-star snark | |
| Vertices | 30 |
| Edges | 45 |
| Radius | 4 |
| Diameter | 4 |
| Girth | 6 |
| Automorphisms | 80 |
| Chromatic number | 3 |
| Chromatic index | 4 |
| Book thickness | 3 |
| Queue number | 2 |
| Properties | Snark Hypohamiltonian |
| Table of graphs and parameters | |
In the mathematical field of graph theory, the double-star snark is a snark with 30 vertices and 45 edges. [1]
Mathematics includes the study of such topics as quantity, structure, space, and change.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices which are connected by edges. A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges, then called arrows, link two vertices asymmetrically; see Graph for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics.
In the mathematical field of graph theory, a snark is a simple, connected, bridgeless cubic graph with chromatic index equal to 4. In other words, it is a graph in which every vertex has three neighbors, the connectivity is redundant so that removing no one edge would split the graph, and the edges cannot be colored by only three colors without two edges of the same color meeting at a point. In order to avoid trivial cases, snarks are often restricted to have girth at least 5.
In 1975, Rufus Isaacs introduced two infinite families of snarks—the flower snark and the BDS snark, a family that includes the two Blanuša snarks, the Descartes snark and the Szekeres snark (BDS stands for Blanuša Descartes Szekeres). [2] Isaacs also discovered one 30-vertex snark that does not belongs to the BDS family and that is not a flower snark — the double-star snark.
Rufus Philip Isaacs was a game theorist especially prominent in the 1950s and 1960s with his work on differential games.
In the mathematical field of graph theory, the flower snarks form an infinite family of snarks introduced by Rufus Isaacs in 1975.
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 Yugoslavian mathematician Danilo Blanuša in 1946 and are named after him. When discovered, only one snark was known—the Petersen graph.
As a snark, the double-star graph is a connected, bridgeless cubic graph with chromatic index equal to 4. The double-star snark is non-planar and non-hamiltonian but is hypohamiltonian. [3] It has book thickness 3 and queue number 2. [4]
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.
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. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points.
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.
