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The set of all the automorphisms of a graph is a group for the composition. For both Loupekine snarks, this group is the dihedral group D 6 {\displaystyle D_{6}} (identified as [12,4] in the Small Groups Database).
In the mathematical field of graph theory, the Robertson–Wegner graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Neil Robertson and Gerd Wegner. [ 2 ] [ 3 ] [ 4 ] It is one of the four (5,5)-cage graphs , the others being the Foster cage , the Meringer graph , and the Wong graph .
When discovered, only one snark was known—the Petersen graph. As snarks, the Blanuša snarks are connected, bridgeless cubic graphs with chromatic index equal to 4. Both of them have chromatic number 3, diameter 4 and girth 5. They are non-hamiltonian but are hypohamiltonian. [4] Both have book thickness 3 and queue number 2. [5]
The incomparability graph of a poset is the graph with vertices given by the elements of which includes an edge between two vertices if and only if their corresponding elements in are incomparable. Conjecture (Stanley–Stembridge) Let G {\displaystyle G} be the incomparability graph of a ( 3 + 1 ) {\textstyle (3+1)} -free poset, then X G ...
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
Graph (discrete mathematics), a structure made of vertices and edges Graph theory, the study of such graphs and their properties; Graph (topology), a topological space resembling a graph in the sense of discrete mathematics; Graph of a function; Graph of a relation; Graph paper; Chart, a means of representing data (also called a graph)
In the mathematical field of graph theory, the Meredith graph is a 4-regular undirected graph with 70 vertices and 140 edges discovered by Guy H. J. Meredith in 1973. [1]The Meredith graph is 4-vertex-connected and 4-edge-connected, has chromatic number 3, chromatic index 5, radius 7, diameter 8, girth 4 and is non-Hamiltonian. [2]
It has chromatic number 3, chromatic index 3, girth 4 and diameter 8. The Tutte graph is a cubic polyhedral graph, but is non-hamiltonian. Therefore, it is a counterexample to Tait's conjecture that every 3-regular polyhedron has a Hamiltonian cycle. [2] Published by Tutte in 1946, it is the first counterexample constructed for this conjecture. [3]