Ad
related to: cubic graph with 9 edges and 6 numbers x and 3 digits answer
Search results
Results From The WOW.Com Content Network
, is a graph with six vertices and nine edges, often referred to as the utility graph in reference to the problem. [1] It has also been called the Thomsen graph after 19th-century chemist Julius Thomsen. It is a well-covered graph, the smallest triangle-free cubic graph, and the smallest non-planar minimally rigid graph.
Roughly speaking, each vertex represents a 3-jm symbol, the graph is converted to a digraph by assigning signs to the angular momentum quantum numbers j, the vertices are labelled with a handedness representing the order of the three j (of the three edges) in the 3-jm symbol, and the graph represents a sum over the product of all these numbers ...
According to Brooks' theorem every connected cubic graph other than the complete graph K 4 has a vertex coloring with at most three colors. Therefore, every connected cubic graph other than K 4 has an independent set of at least n/3 vertices, where n is the number of vertices in the graph: for instance, the largest color class in a 3-coloring has at least this many vertices.
The cube-connected cycles of order n (denoted CCC n) can be defined as a graph formed from a set of n2 n nodes, indexed by pairs of numbers (x, y) where 0 ≤ x < 2 n and 0 ≤ y < n. Each such node is connected to three neighbors: ( x , ( y + 1) mod n ) , ( x , ( y − 1) mod n ) , and ( x ⊕ 2 y , y ) , where "⊕" denotes the bitwise ...
There exist 3 distinct (3,10)-cages, the other two being the Harries graph and the Harries–Wong graph. [5] Moreover, the Harries–Wong graph and Harries graph are cospectral graphs. The Balaban 10-cage has chromatic number 2, chromatic index 3, diameter 6, girth 10 and is hamiltonian. It is also a 3-vertex-connected graph and 3-edge-connected.
The smallest cubic graphs with crossing numbers 1–11 are known (sequence A110507 in the OEIS). The smallest 1-crossing cubic graph is the complete bipartite graph K 3,3, with 6 vertices. The smallest 2-crossing cubic graph is the Petersen graph, with 10 vertices. The smallest 3-crossing cubic graph is the Heawood graph, with 14 vertices
every cubic bridgeless graph without Petersen minor has a cycle double cover. [13] is the smallest cubic graph with Colin de Verdière graph invariant μ = 5. [14] is the smallest graph of cop number 3. [15] has radius 2 and diameter 2. It is the largest cubic graph with diameter 2. [b] has 2000 spanning trees, the most of any 10-vertex cubic ...
In the mathematical field of graph theory, the Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph : every vertex touches exactly three edges. It was discovered by Marion C. Gray in 1932 (unpublished), then discovered independently by Bouwer 1968 in reply to a question posed by Jon Folkman 1967.