CSCE 350 Graphs and Trees

Parent

(u, v) u is said to be the parent of v

Child

(u, v) u is said to be the parent of v and v is the child

Digraphs

A directed graph. A graph whos every edge is directed

Forest

A graph that has no cycles but is not necessarily connected

Complete

A graph with every pair of its vertices connected by an edge

Sparse Graph

A graph with few edges relative to the number of vertices

Acyclic

A graph with no cycles. No path starts and ends at the same vertex

Weighted Graph

A graph with numbers assigned to its edges

Dense Graph

A graph with relatively few possible edges missing

Path

A path from vertex u to vertex v can be defined as a sequence of adjacent vertices that start at u and end with v

Ancestors

All the vertices on the simple path from the root to the particular vertex

Simple Path

All vertices of the graph are distinct

Connected

If for every pair of vertices u and v there is a path from u to v

Cycle

Is a path of a positive length that starts and ends at the same vertex and does not traverse the same edge more than once

Tree

Is acyclic graph

FCNS First Child Next Sibling

Left pointer points to the first child of the vertex and the right pointer points to the next sibling

Length

Length of a path is the total number of vertices in path minus one. Equal to the number of edges in the path

Binary Search Tree

Numbers assigned to each parental vertex is larger than all the numbers of the left sub tree and smaller than the numbers in the right sub tree.

Leaf

Vertex with no children