Graph Theory & Applications 2 min read
Binomial theorem
Binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may be expressed as the sum…
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Graph Theory & Applications 2 min read
Pascal’s Identity
Pascal’s identity, first derived by Blaise Pascal in 17th century, states that the number of ways to choose k elements from…
Graph Theory & Applications 5 min read
Permutations
A permutation is an arrangement of some elements in which order matters. In other words a Permutation is an ordered Combination of…
Graph Theory & Applications 1 min read
Spanning Tree of a Graph
Spanning tree of a graph is a subgraph of it which forms a tree and contains (or spans) all the vertices…
Graph Theory & Applications 8 min read
The Inclusion-Exclusion Principle
From the First Principle of Counting we have arrived at the commutativity of addition, which was expressed in convenient mathematical notations as a + b = b + a. The Principle itself…
Graph Theory & Applications 2 min read
Rooted Trees
A rooted tree is a tree with a special vertex labelled as the “root” the of tree. The root serves as a…
Graph Theory & Applications 2 min read
Chromatic Number
Chromatic number of a graph is the minimum value of kk for which the graph is k-colorablek-colorable. In other words, it is the minimum…
Graph Theory & Applications 3 min read
Non-planar Graphs
Not all graphs are planar. If there are too many edges and too few vertices, then some of the edges…
Graph Theory & Applications 3 min read
Planar Graphs
When is it possible to draw a graph so that none of the edges cross? If this is possible, we say the…
Graph Theory & Applications 4 min read
Mathematics | Euler and Hamiltonian Paths
Certain graph problems deal with finding a path between two vertices such that each edge is traversed exactly once, or…