# online classes

## Inorder Predecessor of node in Binary Tree Using Parent Pointer

Introduction This is the seventh article in the Tree Traversals - Online Classes. This article presents ways to find out inorder predecessor of node in binary tree. As we have already read about the Inorder Successor it wont take much effort to understand the predecessor. Definition - Inorder Predecessor of node in Binary Tree If a node K is called the inorder predecessor of node N then N must be visited immediately after K in a inorder traversal of the tree. Below is a more formal definition of Inorder Predecessor: If the node has a left sub-tree, then inorder predecessor is the ...

## Complex Graph Operations

Introduction This is the fourth article in the Graph Theory - Online Classes. After learning the basic graph operations, its time to dive deeper and have some understanding about the complex operations which we can be done over a graph or a set of graphs. To learn about the basics you can always visit Graph Theory Basics. Complex Graph Operations Union of Graphs The union of two graphs G(VG, EG) and H(VH, EH) is the union of their vertex sets and their edge families. Which means G ∪ H = (VG ∪ VH, EG ∪ EH). The below image shows a union of graph G and graph H. Make sure that all the v...

## Graph Operations

Introduction This is the third article in the Graph Theory - Online Classes. With some basic concepts we learnt in the previous two articles listed here in Graph Theory, now we have enough tools to discuss some operations on any graph. In this article we will try to define some basic operations on the Graph. Graph Operations - Extracting sub graphs In this section we will discuss about various types of sub graphs we can extract from a given Graph. Sub graph Getting a sub graph out of a graph is an interesting operation. A sub graph of a graph G(V,E) can be obtained by the following...

## Special Graphs

Introduction This is the second article in the Graph Theory - Online Classes. Dear readers, I assume that you have already finished reading the first post, if not I would advise you to please go through the first article in the series Introduction to Graph Theory, as this post will require some basic knowledge which we discussed in the previous post. Few Special Graphs The Null Graph The first graph we will discuss is the Null Graph. By definition, this graph has a V(G) which is non-empty and a E(G) which is empty. In simple words a graph which only has vertices and no edges is a Null...

## Graph Theory

Preface This is the first article in the Graph Theory - Online Classes. To all my readers and friends, you can safely skip the first two paragraphs. The motivation to write this series Its been long I have been planning to write this article and now I think is the right time to start a new category & series of articles in the Graph Theory. As a student it was always the most complicated topic for me and I was scared with the topic. I am sure many of you must have faced the same. Of course everyone has their own reason, for me it was the order in which it was taught and definitely it w...