A vertex cut C of a connected graph G(V, E) is a set such that
G C is disconnected.
A u, v-separator for vertices u, v V is a vertex cut which separates u from v.
(u, v) denotes the minimum number of vertices in an (u, v)separator.
A digraph or directed graph G is a triple comprised of a vertex
set V (G), edge set E(G), and a function assigning each edge an
ordered pair of vertices (tail, head); these vertices together are
called endpoints of the edge. We say t
A graph is connected if for any two vertices x, y V (G), there is
a path whose endpoints are x and y.
A connected graph G is called 2-connected, if for every vertex
x V (G), G x is connected.
Matchings in Graphs
Two edges are called independent if they are not adjacent in the
graph. A set of mutually independent edges is called a matc
A graph is called a tree, if it is connected and has no cycles. A star
is a tree with one vertex adjacent to all other vertices.
For every simple graph G with n 1 vertices, the following four
properties are equivalent
(A) G is connected
Matchings in Graphs: compendium of denitions
Denition 1 Two edges are called independent if they are not
adjacent in the graph. A set of mutually independent edges is
called a matching.
A matching is called maximal, if no other matching contai
Basic Denitions (continued with some repeats).
Let d = cfw_d1, d2, . . . , dn be the sequence of degrees of a graph G.
di = 2|E(G)|.
A vertex v (resp. an edge e) in a connected graph is called an articulation point, or a cut vertex (resp. a c
Graph Theory is a delightful playground
for the exploration of proof technique
in discrete mathematics, and its results
have applications in many areas of the
computing, social, and natural sciences.
D. West, Introduction to Graph Theory
Minimum Spanning Trees (MST)
A graph H(U, F ) is a subgraph of G(V, E) if U V and F E.
A subgraph H(U, F ) is called spanning if U = V .
Let G be a graph with weights assigned to