Search results
What is Graph Theory? The study of graphs as mathematical structures G = (V ; E) used to model pairwise relations (a.k.a. edges) between objects of a collection V . The objects are modeled as nodes (or vertices) of a set V The pairwise relations are modeled as edges, which are elements of a set E.
We now define some terminologies related to distances in graphs. The total distance of a vertex v ∈ V(G) is d(v) = ∑u∈V d(u, v). The average distance of a vertex d(v) v ∈ V(G) is d(v) ̄ = |G|−1. = . = uc. = s. such that, ecc(v) = diam(G). The following theorem describes the proper relationship between the r. Theorem 2.1.2. G) ≤.
The distance between two vertices in a graph is a simple but surprisingly useful notion. It has led to the definition of several graph parameters such as the diameter, the radius, the average distance and the metric dimension.
set of all points on above segments, and the distance between two points is the length of the shortest, along the line segments traversed, path connecting them. Also, it can be seen as one-dimensional Riemannian manifold with singularities.
graphs, matchings of graphs, flows on networks (networks are graphs with extra data), and take a closer look at certain types of graphs such as trees and tournaments.
We can compute the distance (in edges) between any two nodes of a graph. Breadth- rst and depth- rst searches are used to \read" the information in a graph. A weighted graph assigns a length to each edge. We can compute the shortest distance between two nodes in a weighted graph.
Abstract. The detour distance between two vertices u and v in a connected graph G is the length of a longest u − v path in G. We survey results and some open questions on detour distance, including connections of this distance to domination, coloring and Hamiltonian properties of graphs.
