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Discrete Mathematics
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Terms in this set (24)
Graph
A graph G = (V, E) consists of V, a nonempty set of vertices (or nodes), and E, a set of edges
Edge and its Endpoints
Each edge has either one or two vertices associated with it, called its endpoints. An edge is said to connect its endpoints
Edge
an unordered pair of vertices
simple graph
A graph G is called a simple graph if G has no loop and no multiple edges
Adjacent
Two vertices u and v in a graph G are called adjacent in G if u and v are endpoints of an edge of G.
incident with
edge that connects two adjacent vertices
Degree of a vertex in a graph
the number of edges incident with it, except that a loop at a vertex contributes twice to the degree of that vertex
isolated vertex
a vertex of degree zero is called isolated
pendant vertex
a vertex of degree one is called pendant
Complete graph (clique)
A complete graph on n vertices, denoted by Kn is a simple graph that contains exactly one edge between each pair of distinct vertices
Empty graph
a graph with no edges
Cycle (circuit)
A cycle Cn, n >= 3, consists of n vertices v1, v2, v3, vn, and edges v1v2, v2v3, vnv1
Subgraph
A subgraph of a graph G is a graph H = (W, F), where W is in V and F is in E
A walk of length n
A walk of length n from u to v is an alternating sequence of vertices and edges of a graph, v0, e1, v1, e2, vn-1, en, vn, where ei = vi-1vi, v0 = u, vn = v, i = 1, 2, 3, n
Path
Path is a walk that has no repeated edge with no repeated vertices
connected graph
A graph is called connected if there is a path between every pair of distinct vertices of the graph
disconnected
A graph is called disconnected if it is not connected
connected component
A connected component of graph G is a connected subgraph of G that is not a proper subgraph of another connected subgraph of G
Tree
a tree is a connected graph with no cycles
leaf
a vertex of degree one in a tree is called a leaf
spanning tree
A spanning tree of G (simple graph) is a subgraph of G that contains every vertex of G
minimum spanning tree
a minimum spanning tree in a connected weighted graph is a spanning tree that has the smallest possible sum of weights of its edges
bipartite graph
a graph is bipartite if its nodes can be partitioned into two classes, say A and B so that every edge connects a node in A to a node in B
perfect matching
a perfect matching is a set of edges such that every node is incident with exactly one of them
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