Graph Theory & Applications
Exponential Generating Functions
Example .1 Find an exponential generating function for the number of permutations with repetition of length nn of…
Graph Theory & Applications
Pólya–Redfield Counting
We have talked about the number of ways to properly color a graph with kk colors, given…
Graph Theory & Applications
Binomial theorem
Binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may…
Graph Theory & Applications
Pascal’s Identity
Pascal's identity, first derived by Blaise Pascal in 17th century, states that the number of ways…
Graph Theory & Applications
Permutations
A permutation is an arrangement of some elements in which order matters. In other words a Permutation…
Graph Theory & Applications
Spanning Tree of a Graph
Spanning tree of a graph is a subgraph of it which forms a tree and contains…
Graph Theory & Applications
The Inclusion-Exclusion Principle
From the First Principle of Counting we have arrived at the commutativity of addition, which was expressed in convenient…
Graph Theory & Applications
Rooted Trees
A rooted tree is a tree with a special vertex labelled as the "root" the of tree.…
Graph Theory & Applications
Chromatic Number
Chromatic number of a graph is the minimum value of kk for which the graph is k-colorablek-colorable. In other…