Ads
related to: graph endpoints vs edges of triangle shapes worksheet 1 pdf
Search results
Results from the WOW.Com Content Network
In an undirected simple graph of order n, the maximum degree of each vertex is n − 1 and the maximum size of the graph is n(n − 1) / 2 . The edges of an undirected simple graph permitting loops induce a symmetric homogeneous relation on the vertices of that is called the adjacency relation of .
In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. [1]
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).
The edge-connectivity for a graph with at least 2 vertices is less than or equal to the minimum degree of the graph because removing all the edges that are incident to a vertex of minimum degree will disconnect that vertex from the rest of the graph. [1] For a vertex-transitive graph of degree d, we have: 2(d + 1)/3 ≤ κ(G) ≤ λ(G) = d. [11]
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).
When modelling relations between two different classes of objects, bipartite graphs very often arise naturally. For instance, a graph of football players and clubs, with an edge between a player and a club if the player has played for that club, is a natural example of an affiliation network, a type of bipartite graph used in social network analysis.
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G).
For example, applying a YΔ-transformation to a 3-vertex of a planar graph, or a ΔY-transformation to a triangular face of a planar graph, results again in a planar graph. [1] This was used in the original proof of Steinitz's theorem , showing that every 3-connected planar graph is the edge graph of a polyhedron .
Ads
related to: graph endpoints vs edges of triangle shapes worksheet 1 pdf