Ads
related to: graph endpoints vs edges of triangle worksheet printable template freeeducation.com has been visited by 100K+ users in the past month
Education.com is great and resourceful - MrsChettyLife
Search results
Results from the WOW.Com Content Network
The Grötzsch graph is a triangle-free graph that cannot be colored with fewer than four colors. Much research about triangle-free graphs has focused on graph coloring. Every bipartite graph (that is, every 2-colorable graph) is triangle-free, and Grötzsch's theorem states that every triangle-free planar graph may be 3-colored. [8]
An undirected graph with three vertices and three edges. In one restricted but very common sense of the term, [1] [2] a graph is an ordered pair = (,) comprising: , a set of vertices (also called nodes or points);
In addition, for each edge v i v j of G, the Mycielski graph includes two edges, u i v j and v i u j. Thus, if G has n vertices and m edges, μ(G) has 2n+1 vertices and 3m+n edges. The only new triangles in μ(G) are of the form v i v j u k, where v i v j v k is a triangle in G. Thus, if G is triangle-free, so is μ(G).
More precisely one speaks of Shannon multigraph Sh(n), if the three vertices are connected by ⌊ ⌋, ⌊ ⌋ and ⌊ + ⌋ edges respectively. This multigraph has maximum degree n . Its multiplicity (the maximum number of edges in a set of edges that all have the same endpoints) is ⌊ n + 1 2 ⌋ {\displaystyle \left\lfloor {\frac {n+1}{2 ...
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
In the mathematical field of graph theory, the Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number 5. It is named after German mathematician Herbert Grötzsch , who used it as an example in connection with his 1959 theorem that planar triangle-free graphs are 3-colorable.
A directed graph is weakly connected (or just connected [9]) if the undirected underlying graph obtained by replacing all directed edges of the graph with undirected edges is a connected graph. A directed graph is strongly connected or strong if it contains a directed path from x to y (and from y to x) for every pair of vertices (x, y).
A cycle of length three in a graph. A triangle-free graph is an undirected graph that does not have any triangle subgraphs. trivial A trivial graph is a graph with 0 or 1 vertices. [16] A graph with 0 vertices is also called null graph. Turán 1. Pál Turán 2. A Turán graph is a balanced complete multipartite graph. 3.
Ads
related to: graph endpoints vs edges of triangle worksheet printable template freeeducation.com has been visited by 100K+ users in the past month
Education.com is great and resourceful - MrsChettyLife