WebIn graph theory, a -bounded family of graphs is one for which there is some function such that, for every integer the graphs in with = (clique number) can be colored with at most () colors. This concept and its notation were formulated by András Gyárfás. The use of the Greek letter chi in the term -bounded is based on the fact that the chromatic number of a … WebMar 6, 2024 · In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path distance. [1] Notice that there may be more than one shortest path between two vertices. [2]
Graph Radius -- from Wolfram MathWorld
WebThe Petersen graph is the cubic graph on 10 vertices and 15 edges which is the unique (3,5)-cage graph (Harary 1994, p. 175), as well as the unique (3,5)-Moore graph. It can be constructed as the graph expansion of 5P_2 with steps 1 and 2, where P_2 is a path graph (Biggs 1993, p. 119). Excising an edge of the Petersen graph gives the 4-Möbius ladder … Web2 1. Graph Theory At first, the usefulness of Euler’s ideas and of “graph theory” itself was found only in solving puzzles and in analyzing games and other recreations. In the mid 1800s, however, people began to realize that graphs could be used to model many things that were of interest in society. For instance, the “Four Color Map ... polystyrene coving
Introduction to Graphs Types of Graphs - Analytics Vidhya
Webradiusof Gis the minimum eccentricity among the vertices of G. Therefore, radius(G)=min{e(v):vin V(G)}. The diameterof Gis the maximum eccentricity among the vertices of G. Thus, diameter(G)=max{e(v):vin V(G)}. The girthof Gis the length of a shortest cycle in G. The centerof Gis the set of vertices of WebEccentricity, radius and diameter are terms that are used often in graph theory. They are related to the concept of the distance between vertices. The dist... A metric space defined over a set of points in terms of distances in a graph defined over the set is called a graph metric. The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is connected. The eccentricity ϵ(v) of a vertex v is the greatest distance between v and any other vertex; in symbols, polystyrene coving at b\u0026q